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1. Banach space valued neural network : ordinary and fractional approximation and interpolation [2023]
 Anastassiou, George A., 1952 author.
 Cham, Switzerland : Springer, 2023.
 Description
 Book — 1 online resource (xiv, 423 pages) : illustrations.
 Summary

 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 KantorovichChoquet quasiinterpolation neural network operators revisited. Quantitative Approximation by KantorovichShilkret quasiinterpolation neural network operators revisited. Voronsovkaya Univariate and Multivariate asymptotic expansions for sigmoid functions induced quasiinterpolation 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 FuzzyRandom and stochastic various activation functions activated Neural Network Approximations.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952
 Cham, Switzerland : Springer, 2022.
 Description
 Book — 1 online resource
 Summary

 Basic abstract fractional monotone approximation. Abstract bivariate left fractional monotone constrained approximation by pseudopolynomials. Conclusion.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952 author.
 Cham, Switzerland : Springer, 2022.
 Description
 Book — 1 online resource (xiii, 307 pages) : illustrations.
 Summary

 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 HilbertPachpatte inequalities for Banach algebra valued functions. Generalized Ostrowski, Opial and Hilbertachpatte inequalities for Banach algebra valued functions involving integer vectorial derivatives.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952 author.
 Cham, Switzerland : Springer, [2022]
 Description
 Book — 1 online resource (xi, 419 pages) Digital: text file.PDF.
 Summary

 Progress on generalized Hilfer fractional calculus and fractional integral inequalities. Landau Generalized Hilfer fractional inequalities. IyengarHilfer generalized fractional inequalities. Generalized HilferPolya, HilferOstrowski and HilferHilbertPachpatte fractional inequalities. Generalized Hilfer Fractional Approximation of Csiszar's fDivergence. Generalized Hilfer fractional selfadjoint operator inequalities. Essential forward and reverse generalized HilferHardy fractional inequalities. Principles of Generalized PrabhakarHilfer fractional Calculus and Applications.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952
 Cham : Springer, 2021.
 Description
 Book — 1 online resource (523 pages)
 Summary

 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 RiemannLiouville type. Generalized Canavati fractional Landau inequalities. Sequential left abstract fractional Landau inequalities. Iterated left abstract generalized fractional Landau inequalities.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952 author.
 Cham : Springer, [2021]
 Description
 Book — 1 online resource (xv, 498 pages) Digital: PDF.text file.
 Summary

 Caputo fractional Ostrowski inequalities. Caputo fractional Ostrowski and Gruss inequalities involving several functions. Weighted Caputo fractional Iyengar type inequalities. Generalized Canavati gfractional Iyengar and Ostrowski inequalities. Generalized Canavati gfractional Polya inequalities. Caputo generalized fractional integral type inequalities. Generalized fractional Quantitative Approximation by Sublinear Operators. Generalized giterated fractional Quantitative Approximation by Sublinear Operators. Generalized gFractional vector Representation Formula and Bochner integral type inequalities for Banach space valued functions. Iterated gFractional vector Bochner integral Representation Formulae and inequalities for Banach space valued functions. Vectorial generalized gfractional direct and iterated Quantitative Approximation by linear operators. Quantitative Multivariate Complex Korovkin Approximation Theory. Mfractional 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 ψFractional Ostrowski Inequalities
 Caputo ψFractional Ostrowski and Grüss Inequalities
 Weighted Caputo Fractional Iyengar Type Inequalities
 Generalized Canavati gFractional Iyengar and Ostrowski Inequalities
 Generalized Canavati gFractional Polya Inequalities
 Caputo Generalized ψFractional Integral Type Inequalities
 Generalized ψFractional Quantitative Approximation by Sublinear Operators
 Generalized gIterated Fractional Quantitative Approximation By Sublinear Operators
 Generalized gFractional Vector Representation Formula And Bochner Integral Type Inequalities for Banach Space Valued Functions
 Iterated gFractional Vector Bochner Integral Representation Formulae and Inequalities for Banach Space Valued Functions
 Vectorial Generalized gFractional Direct and Iterated Quantitative Approximation by Linear Operators
 Quantitative Multivariate Complex Korovkin Approximation Theory
 MFractional 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.
(source: Nielsen Book Data)
 Anastassiou, George A., 1952
 Cham : Springer, 2020.
 Description
 Book — 1 online resource (xiv, 525 pages) : illustrations
 Summary

 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)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952 author.
 Cham, Switzerland : Springer, [2018]
 Description
 Book — 1 online resource.
 Summary

 ExplicitImplicit 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
 Semilocal convergence in right abstract fractional calculus
 Algorithmic convergence in abstract gfractional calculus
 Iterative procedures for solving equations in abstract fractional calculus
 Approximate solutions of equations in abstract gfractional calculus
 Generating sequences for solving in abstract gfractional calculus
 Numerical Optimization and fractional invexity.
 Anastassiou, George A., 1952 author.
 Cham, Switzerland : Springer, 2018.
 Description
 Book — 1 online resource (x, 319 pages) Digital: text file.PDF.
 Summary

 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)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952
 Singapore : World Scientific Publishing Co. Pte Ltd., c2017.
 Description
 Book — 1 online resource (347 p.) : ill. (some col.)
 Summary

"In this monograph, we present the authors' recent work of the last seven years in Approximation Theory. Chapters are selfcontained 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 nonunitary, 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.
 Anastassiou, George A., 1952 author.
 Cham, Switzerland : Springer, [2017]
 Description
 Book — xii, 224 pages ; 25 cm.
 Summary

 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 ChebyshevGruss Inequalities. Ultra General Fractional Self Adjoint Operator Representation formulae and Operator Poincare and Sobolev and other basic Inequalities. Harmonic Self Adjoint Operator ChebyshevGruss type Inequalities. Ultra general Self Adjoint Operator ChebyshevGruss type Inequalities. About a fractional Means inequality.
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(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA297 .A53 2017  Unknown 
 Anastassiou, George A., 1952
 Singapore : World Scientific Publishing Co. Pte. Ltd., ©2016.
 Description
 Book — 1 online resource (x, 278 p.) : ill.
 Summary

"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 sconvexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite–Hadamard type inequalities using mconvexity 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 selfcontained 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.
 Anastassiou, George A., 1952 author.
 Cham : Springer, 2016.
 Description
 Book — 1 online resource (xv, 662 pages) Digital: text file.PDF.
 Summary

 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 HilbertPachpatte 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)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952 author.
 Switzerland : Springer, 2016.
 Description
 Book — 1 online resource (xii, 116 pages)
 Summary

 Fixed Point Results and Applications in Left Multivariate Fractional Calculus
 Fixed Point Results and Applications in Right Multivariate Fractional Calculus
 Semilocal Iterative Procedures and Applications In KMultivariate Fractional Calculus
 Newtonlike 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 RiemannLiouville Fractional Integral
 The Right Multidimensional RiemannLiouville Fractional Integral.
 Anastassiou, George A., 1952 author.
 Cham : Springer, 2016.
 Description
 Book — 1 online resource (xv, 712 pages) : illustrations Digital: text file.PDF.
 Summary

 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 CardaliaguetEuvrard Neural Networks. Fractional Asymptotic Expansions for Quasiinterpolation 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 FuzzyRandom 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 QuasiInterpolation Neural Networks. Multivariate FuzzyRandom 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. FuzzyRandom 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 FuzzyRandom Perturbed Neural Network Approximations.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Anastassiou, George A., 1952
 Singapore : World Scientific Publishing Co. Pte. Ltd, c2015.
 Description
 Book — 1 online resource (xii, 216 p.) : ill. (some col.)
 Summary

"This monograph presents the author's work of the last five years in approximation theory. The chapters are selfcontained 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.
 Anastassiou, George A., 1952 author.
 Cham : Springer, [2015]
 Description
 Book — 1 online resource (xvi, 423 pages) : color illustrations
 Summary

 NewtonLike Methods on Generalized Banach Spaces and Fractional Calculus
 Semilocal Convegence of NewtonLike Methods and Fractional Calculus
 Convergence of Iterative Methods and Generalized Fractional Calculus
 Fixed Point Techniques And Generalized Right Fractional Calculus
 Approximating Fixed Points And KFractional Calculus
 Iterative Methods And Generalized GFractional 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
 SecantLike Methods And Fractional Calculus
 SecantLike Methods And Modified G Fractional Calculus
 SecantLike Algorithms And Generalized Fractional Calculus
 SecantLike Methods And Generalized GFractional Calculus Of CanavatiType
 Iterative Algorithms And LeftRight Caputo Fractional Derivatives
 Iterative Methods On Banach Spaces With A Convergence Structure And Fractional Calculus
 Inexact GaussNewton 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.
18. Numerical analysis using Sage [2015]
 Anastassiou, George A., 1952 author.
 Cham : Springer, 2015.
 Description
 Book — 1 online resource (xii, 314 pages) : illustrations (some color) Digital: text file.PDF.
 Summary

 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.
 Anastassiou, George A., 1952
 Cham : Springer, [2014]
 Description
 Book — 1 online resource (319 pages) : illustrations Digital: text file.PDF.
 Summary

 Vector Spaces
 Plane And Straight Line In E
 Linear Transformations
 Euclidean Vector Spaces
 Bilinear And Quadratic Forms
 Differential Geometry Of Curves And Surfaces.
20. Intelligent routines : solving mathematical analysis with Matlab, Mathcad, Mathematica and Maple [2013]
 Anastassiou, George A., 1952
 Berlin ; New York : Springer, ©2013.
 Description
 Book — 1 online resource Digital: text file.PDF.
 Summary

 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.
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