%{search_type} search results

• Algebraic function induced Banach space valued ordinary and fractional neural network approximations.- Gudermannian function induced Banach space valued ordinary and fractional neural network approximations.- Generalized symmetrical sigmoid function induced Banach space valued ordinary and fractional neural network approximations.- Abstract multivariate algebraic function induced neural network approximations.- General multivariate arctangent function induced neural network approximations.- Abstract multivariate Gudermannian function induced neural network approximations.- Generalized symmetrical sigmoid function induced neural network multivariate approximation.- Quantitative Approximation by Kantorovich-Choquet quasi-interpolation neural network operators revisited.- Quantitative Approximation by Kantorovich-Shilkret quasi-interpolation neural network operators revisited.- Voronsovkaya Univariate and Multivariate asymptotic expansions for sigmoid functions induced quasi-interpolation neural network operators revisited.- Univariate Fuzzy Fractional various sigmoid function activated neural network approximations revisited.- Multivariate Fuzzy Approximation by Neural Network Operators induced by several sigmoid functions revisited.- Multivariate Fuzzy-Random and stochastic various activation functions activated Neural Network Approximations.
• (source: Nielsen Book Data)

This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book's results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
(source: Nielsen Book Data)

• Basic abstract fractional monotone approximation.- Abstract bivariate left fractional monotone constrained approximation by pseudo-polynomials.- Conclusion.
• (source: Nielsen Book Data)

This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book's results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.
(source: Nielsen Book Data)

• Generalized Fractional Ostrowski and Gruss inequalities with multiple Banach algebra valued functions.- Iterated Generalized Fractional Ostrowski and Gruss inequalities with multiple Banach algebra valued functions.- Generalized Canavati Fractional Ostrowski, Opial and Gruss inequalities with multiple Banach algebra valued functions.- Generalized Canavati Fractional Hilbert-Pachpatte inequalities for Banach algebra valued functions.- Generalized Ostrowski, Opial and Hilbert-achpatte inequalities for Banach algebra valued functions involving integer vectorial derivatives.
• (source: Nielsen Book Data)

This book presents generalized Caputo fractional Ostrowski and Gruss-type inequalities involving several Banach algebra valued functions. Furthermore, the author gives generalized Canavati fractional Ostrowski, Opial, Gruss, and Hilbert-Pachpatte-type inequalities for multiple Banach algebra valued functions. By applying the p-Schatten norms over the von Neumann-Schatten classes, the author produces the analogous refined and interesting inequalities. The author provides many applications. This book's results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications are in applied sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
(source: Nielsen Book Data)

• Progress on generalized Hilfer fractional calculus and fractional integral inequalities.- Landau Generalized Hilfer fractional inequalities.- Iyengar-Hilfer generalized fractional inequalities.- Generalized Hilfer-Polya, Hilfer-Ostrowski and Hilfer-Hilbert-Pachpatte fractional inequalities.- Generalized Hilfer Fractional Approximation of Csiszar's f-Divergence.- Generalized Hilfer fractional self-adjoint operator inequalities.- Essential forward and reverse generalized Hilfer-Hardy fractional inequalities.- Principles of Generalized Prabhakar-Hilfer fractional Calculus and Applications.
• (source: Nielsen Book Data)

This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer-Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert-Pachpatte, Hardy, Opial, Csiszar's f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book's results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners and seminars of the above disciplines, also to be in all science and engineering libraries.
(source: Nielsen Book Data)

• Variable order general fractional integral inequalitie.- Variable order fractional integral inequalities for spherical shell.- Left fractional integral inequalities of E.R. Love type.- Right side fractional integral inequalities of E.R. Love type.- General fractional Landau inequalities.- Abstract fractional Landau inequalities.- Fractional Landau inequalities of Riemann-Liouville type.- Generalized Canavati fractional Landau inequalities.- Sequential left abstract fractional Landau inequalities.- Iterated left abstract generalized fractional Landau inequalities.
• (source: Nielsen Book Data)

This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann-Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert-Pachpatte and on the spherical shell. He continues with E. R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.
(source: Nielsen Book Data)

• Caputo -fractional Ostrowski inequalities.- Caputo -fractional Ostrowski and Gruss inequalities involving several functions.- Weighted Caputo fractional Iyengar type inequalities.- Generalized Canavati g-fractional Iyengar and Ostrowski inequalities.- Generalized Canavati g-fractional Polya inequalities.- Caputo generalized -fractional integral type inequalities.- Generalized -fractional Quantitative Approximation by Sub-linear Operators.- Generalized g-iterated fractional Quantitative Approximation by Sublinear Operators.- Generalized g-Fractional vector Representation Formula and Bochner integral type inequalities for Banach space valued functions.- Iterated g-Fractional vector Bochner integral Representation Formulae and inequalities for Banach space valued functions.- Vectorial generalized g-fractional direct and iterated Quantitative Approximation by linear operators.- Quantitative Multivariate Complex Korovkin Approximation Theory.- M-fractional integral type inequalities.- Principles of Stochastic Caputo Fractional Calculus with Fractional Approximation of Stochastic Processes.- Trigonometric Caputo Fractional Approximation of Stochastic Processes.- Trigonometric Conformable Fractional Approximation of Stochastic Processe.- Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes.- Trigonometric Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes.- Commutative Conformable Fractional Korovkin Approximation for Stochastic Processes.- Trigonometric Commutative Conformable Fractional Korovkin Approximation for Stochastic Processes.- Concluding Remarks.
• (source: Nielsen Book Data)

• Caputo ψ-Fractional Ostrowski Inequalities
• Caputo ψ-Fractional Ostrowski and Grüss Inequalities
• Weighted Caputo Fractional Iyengar Type Inequalities
• Generalized Canavati g-Fractional Iyengar and Ostrowski Inequalities
• Generalized Canavati g-Fractional Polya Inequalities
• Caputo Generalized ψ-Fractional Integral Type Inequalities
• Generalized ψ-Fractional Quantitative Approximation by Sublinear Operators
• Generalized g-Iterated Fractional Quantitative Approximation By Sublinear Operators
• Generalized g-Fractional Vector Representation Formula And Bochner Integral Type Inequalities for Banach Space Valued Functions
• Iterated g-Fractional Vector Bochner Integral Representation Formulae and Inequalities for Banach Space Valued Functions
• Vectorial Generalized g-Fractional Direct and Iterated Quantitative Approximation by Linear Operators
• Quantitative Multivariate Complex Korovkin Approximation Theory
• M-Fractional Integral Type Inequalities
• Principles of Stochastic Caputo Fractional Calculus with Fractional Approximation of Stochastic Processes
• Trigonometric Caputo Fractional Approximation of Stochastic Processes
• Conformable Fractional Quantitative Approximation of Stochastic Processes
• Trigonometric Conformable Fractional Approximation of Stochastic Processes
• Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes
• Trigonometric Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes
• Commutative Conformable Fractional Korovkin Approximation for Stochastic Processes
• Trigonometric Commutative Conformable Fractional Korovkin Approximation for Stochastic Processes
• Concluding Remarks.

This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.
(source: Nielsen Book Data)

• General Ordinary Iyengar Inequalities.- Caputo fractional Iyengar Inequalities.- Canavati fractional Iyengar Inequalities.- General Multivariate Iyengar inequalities.- Multivariate Iyengar inequalities for radial functions.- Multidimensional Fractional Iyengar inequalities for radial functions.- General Multidimensional Fractional Iyengar inequalities.- Delta Time Scales Iyengar Inequalities.
• (source: Nielsen Book Data)

This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann-Liouville type and related results including inequalities. We examine the case of low order Riemann-Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar's well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.
(source: Nielsen Book Data)

• Explicit-Implicit methods with applications to Banach space valued functions in abstract fractional calculus
• Convergence of Iterative methods in abstract fractional calculus
• Equations for Banach space valued functions in fractional vector calculi
• Iterative methods in abstract fractional calculus
• Semi-local convergence in right abstract fractional calculus
• Algorithmic convergence in abstract g-fractional calculus
• Iterative procedures for solving equations in abstract fractional calculus
• Approximate solutions of equations in abstract g-fractional calculus
• Generating sequences for solving in abstract g-fractional calculus
• Numerical Optimization and fractional invexity.

• A strong left Fractional Calculus for Banach space valued functions.- Strong Right Abstract Fractional Calculus.- Strong mixed and generalized Abstract Fractional Calculus.- Foundations of General Fractional Analysis for Banach space valued functions.- Vector abstract fractional Korovkin Approximation.- Basic Abstract Korovkin theory.- High Approximation for Banach space valued functions.- Vectorial abstract fractional approximation using linear operators.- Abstract fractional trigonometric Korovkin approximation.- Multivariate Abstract Approximation for Banach space valued functions.- Arctangent function based Abstract Neural Network approximation. .
• (source: Nielsen Book Data)

This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book's results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book's results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.
(source: Nielsen Book Data)

"In this monograph, we present the authors' recent work of the last seven years in Approximation Theory. Chapters are self-contained and can be read independently and advanced courses can be taught out of this book. Here our generalized discrete singular operators are of the following types: Picard, Gauss–Weierstrass and Poisson–Cauchy operators. We treat both the unitary and non-unitary, univariate and multivariate cases of these operators, which are not necessarily positive operators. The book's results are expected to find applications in many areas of pure and applied mathematics, and statistics. As such, it is suitable for researchers, graduate students, and seminars of related subjects, and serves well as an invaluable resource for all science libraries."--Publisher's website.

• Preface.- Self Adjoint Operator Korovkin type Quantitative Approximation Theory.- Self Adjoint Operator Korovkin and polynomial direct Approximations with rates.- Quantitative Self Adjoint Operator other Direct Approximations.- Fractional Self Adjoint Operator Poincare and Sobolev Inequalities.- Self Adjoint Operator Ostrowski Inequalities.- Integer and Fractional Self Adjoint Operator Opial Inequalities.- Self Adjoint Operator Chebyshev-Gruss Inequalities.- Ultra General Fractional Self Adjoint Operator Representation formulae and Operator Poincare and Sobolev and other basic Inequalities.- Harmonic Self Adjoint Operator Chebyshev-Gruss type Inequalities.- Ultra general Self Adjoint Operator Chebyshev-Gruss type Inequalities.- About a fractional Means inequality.
• (source: Nielsen Book Data)

This compact book focuses on self-adjoint operators' well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book's results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
(source: Nielsen Book Data)

"This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite–Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied. This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries."-- Provided by publisher.

• Fractional Polya Integral Inequality.- Univariate Fractional Polya Integral Inequalities.- About Multivariate General Fractional Polya Integral Inequalities.- Balanced Canavati Fractional Opial Inequalities.- Fractional Representation Formulae and Fractional Ostrowski Inequalities.- Basic Fractional Integral Inequalities.- Harmonic Multivariate Ostrowski and Gruss Inequalities.- Fractional Ostrowski and Gruss Inequalities Using Several Functions.- Further Interpretation of Some Fractional Ostrowski and Gruss Type Inequalities.- Multivariate Fractional Representation Formula and Ostrowski Inequality.- Fractional Representation Formulae and Ostrowski Inequalities.- About Multivariate Lyapunov Inequalities.- Ostrowski Type Inequalities for Semigroups.- About Ostrowski Inequalities for Cosine and Sine Operator Functions.- About Hilbert-Pachpatte Inequalities.- About Ostrowski and Landau Type Inequalities.- Multidimensional Ostrowski Type Inequalities.- About Fractional Representation Formulae and Right Fractional Inequalities.- About Canavati fractional Ostrowski inequalities.- The Most General Fractional Representation Formula.- Rational Inequalities for Integral Operators Using Convexity.- Fractional Integral Inequalities with Convexity.- Vectorial Inequalities for Integral Operators.- Vectorial Splitting Rational Lp Inequalities for Integral Operators.- Separating Rational Lp Inequalities for Integral Operators.- About Vectorial Hardy Type Fractional Inequalities.- About Vectorial Fractional Integral Inequalities Using Convexity.
• (source: Nielsen Book Data)

This monograph presents recent and original work of the author on inequalities in real, functional and fractional analysis. The chapters are self-contained and can be read independently, they include an extensive list of references per chapter. The book's results are expected to find applications in many areas of applied and pure mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, as well as Science and Engineering University libraries.
(source: Nielsen Book Data)

• Fixed Point Results and Applications in Left Multivariate Fractional Calculus
• Fixed Point Results and Applications in Right Multivariate Fractional Calculus
• Semi-local Iterative Procedures and Applications In K-Multivariate Fractional Calculus
• Newton-like Procedures and Applications in Multivariate Fractional Calculus
• Implicit Iterative Algorithms and Applications in Multivariate Calculus
• Monotone Iterative Schemes and Applications in Fractional Calculus
• Extending the Convergence Domain of Newton?s Method
• The Left Multidimensional Riemann-Liouville Fractional Integral
• The Right Multidimensional Riemann-Liouville Fractional Integral.

In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. An extensive list of references is given per chapter. The book?s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.

• Rate of Convergence of Basic Neural Network Operators to the Unit.- Rate of Convergence of Basic Multivariate Neural Network Operators.- Fractional Neural Network Operators Approximation.- Fractional Approximation Using Cardaliaguet-Euvrard Neural Networks.- Fractional Asymptotic Expansions for Quasi-interpolation neural Networks.- Voronovskaya Type Asymptotic Expansions for Multivariate Neural Networks.- Fractional Approximation by Bell and Squashing Neural Networks.- Fractional Asymptotic Expansions For Bell And Squashing Neural Networks.- Multivariate Asymptotic Expansions for Bell and Squashing Neural Networks.- Multivariate Fuzzy-Random Normalized Neural Network Approximation.- Fuzzy Fractional Approximations by Fuzzy Bell and Squashing Neural Networks.- Fuzzy Fractional Neural Network Approximation.- Multivariate Fuzzy Approximation Using Basic Neural Network Operators.- Multivariate Fuzzy Approximation Using Quasi-Interpolation Neural Networks.- Multivariate Fuzzy-Random Neural Networks Approximation.- Approximation by Kantorovich and Quadrature type neural Networks.- Univariate Error Function Based Neural Network Approximations.- Multivariate Error Function Based Neural Network Operators Approximation.- Asymptotic Expansions for Error Function Based Neural Networks.- Fuzzy Fractional Error Function Relied Neural Network Approximations.- Multivariate Fuzzy Approximation by Neural Networks.- Fuzzy-Random Error Function Relied Neural Network Approximations.- Approximation by Perturbed Neural Networks.- Approximations by Multivariate Perturbed Neural Networks.- Voronovskaya type Asymptotic Expansions for Perturbed Neural Networks.- Approximation using Fuzzy Perturbed Neural Networks.- Multivariate Fuzzy Perturbed Neural Network Approximations.- Multivariate Fuzzy-Random Perturbed Neural Network Approximations.
• (source: Nielsen Book Data)

This monograph is the continuation and completion of the monograph, "Intelligent Systems: Approximation by Artificial Neural Networks" written by the same author and published 2011 by Springer. The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book's results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries.
(source: Nielsen Book Data)

"This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss–Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries."-- Provided by publisher.

• Newton-Like Methods on Generalized Banach Spaces and Fractional Calculus
• Semilocal Convegence of Newton-Like Methods and Fractional Calculus
• Convergence of Iterative Methods and Generalized Fractional Calculus
• Fixed Point Techniques And Generalized Right Fractional Calculus
• Approximating Fixed Points And K-Fractional Calculus
• Iterative Methods And Generalized G-Fractional Calculus
• Unified Convergence Analysis For Iterative Algorithms And Fractional Calculus
• Convergence Analysis For Extended Iterative Algorithms And Fractional And Vector Calculus
• Convergence Analysis For Extended Iterative Algorithms And Fractional Calculus
• Secant-Like Methods And Fractional Calculus
• Secant-Like Methods And Modified G- Fractional Calculus
• Secant-Like Algorithms And Generalized Fractional Calculus
• Secant-Like Methods And Generalized G-Fractional Calculus Of Canavati-Type
• Iterative Algorithms And Left-Right Caputo Fractional Derivatives
• Iterative Methods On Banach Spaces With A Convergence Structure And Fractional Calculus
• Inexact Gauss-Newton Method For Singular Equations
• The Asymptotic Mesh Independence Principle
• Ball Convergence Of A Sixth Order Iterative Method
• Broyden's Method With Regularily Continuous Divided Differences
• Left General Fractional Monotone Approximation
• Right General Fractional Monotone Approximation Theor
• Left Generalized High Order Fractional Monotone Approximation
• Right Generalized High Order Fractional Monotone Approximation
• Advanced Fractional Taylor's Formulae
• Generalized Canavati Type Fractional Taylor's Formulae.

In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book's results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

• Preface
• 1. Fundamentals
• 2. Solving Nonlinear Equations
• 3. Polynomial Interpolation
• 4. Numerical Differentiation
• 5. Numerical Integration
• 6. Spline Interpolation
• 7. Numerical Methods for Differential Equations
• References
• Index.

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application. Answers may be verified using Sage. The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®. Sage is open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a plus. Moreover, the code can be written using any web browser and is therefore useful with Laptops, Tablets, iPhones, Smartphones, etc. All Sage code that is presented in the text is openly available on SpringerLink.com.

• Vector Spaces
• Plane And Straight Line In E
• Linear Transformations
• Euclidean Vector Spaces
• Bilinear And Quadratic Forms
• Differential Geometry Of Curves And Surfaces.

"Intelligent Routines II: Solving Linear Algebra and Differential Geometry with Sage" contains numerous of examples and problems as well as many unsolved problems. This book extensively applies the successful software Sage, which can be found free online http://www.sagemath.org/. Sage is a recent and popular software for mathematical computation, available freely and simple to use. This book is useful to all applied scientists in mathematics, statistics and engineering, as well for late undergraduate and graduate students of above subjects. It is the first such book in solving symbolically with Sage problems in Linear Algebra and Differential Geometry. Plenty of SAGE applications are given at each step of the exposition.

• Sequences and Series of Numbers
• Power Series
• Differentiation Theory of the Functions
• Fundamentals of Field Theory
• Implicit Functions
• Terminology about Integral Calculus
• Equations and Systems of Linear Ordinary Differential Equations
• Line and Double Integral Calculus
• Triple and Surface Integral Calculus.

Real Analysis is a discipline of intensive study in many institutions of higher education, because it contains useful concepts and fundamental results in the study of mathematics and physics, of the technical disciplines and geometry. This book is the first one of its kind that solves mathematical analysis problems with all four related main software Matlab, Mathcad, Mathematica and Maple. Besides the fundamental theoretical notions, the book contains many exercises, solved both mathematically and by computer, using: Matlab 7.9, Mathcad 14, Mathematica 8 or Maple 15 programming languages. The book is divided into nine chapters, which illustrate the application of the mathematical concepts using the computer. Each chapter presents the fundamental concepts and the elements required to solve the problems contained in that chapter and finishes with some problems left to be solved by the readers. The calculations can be verified by using a specific software such as Matlab, Mathcad, Mathematica or Maple.