George A. Anastassiou - Banach Space Valued Neural Network: Ordinary and Fractional Approximation and Interpolation (Studies in Computational Intelligence, 1062)

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This monograph is the continuation of authors earlier (i) 2011 monograph, Intelligent Systems: Approximation by Artificial Neural Networks, Springer, Intelligent Systems Reference Library, Volume 19, and (ii) 2016 monograph, Intelligent Systems II: Complete Approximation by Neural Network Operators, Studies in Computational Intelligence, Volume 608.

The innovation here is that the neural networks are Banach space valued, induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian and generalized symmetric sigmoid functions.

Thus, in this monograph, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. We exhibit univariate, fractional and multivariate approximations. Iterated-sequential approximations are also studied. The new and important feature here is that the functions under approximation are Banach space valued.

As a result, this monograph is the natural and expected evolution of recent authors research work put in a book form for the first time. The presented approaches are original, and the chapters are self-contained and can be read independently. This monograph is suitable to be used in related graduate classes and research projects.

The motivation to write this monograph came from the following: various issues related to the modeling and analysis of ordinary and fractional order systems have gained an increased popularity, as witnessed by many books and volumes in Springers program: http://www.springer.com/gp/search?query=fractional&submit=Prze%C5%9Blij and the purpose of our book is to capture at a very general level a deeper formal analysis on some issues that are relevant to many areas, for instance: decision-making, complex processes, systems modeling and control and related areas.

The above are deeply embedded in the fields of mathematics, engineering, computer science, physics, economics, social and life sciences.