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.

Autorentext

George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including "Fractional Differentiation Inequalities" (c) 2009, "Fuzzy Mathematics: Approximation Theory" (c) 2010, "Intelligent Systems: Approximation by Artificial Neural Networks" (c) 2014, "The History of Approximation Theory" (c) 2005, "Modern Differential Geometry in Gauge Theories" (c) 2006, and more. Razvan Alex Mezei received his PhD from the University of Memphis and currently holds an assistant professorship and Lenoir-Rhyne University, Hickory, North Carolina. He teaches mathematics as well as computer science/IT courses to undergraduates and is a computing sciences program coordinator. Mezei has extensive experience in computer programming and software development and has written several publications with George Anastassiou.

Inhalt
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-interpolationneural 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.