Bøger af George A. Anastassiou

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.

In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, 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. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.

This book presents generalized Caputo fractional Ostrowski and Grüss-type inequalities involving several Banach algebra valued functions. Furthermore, the author gives generalized Canavati fractional Ostrowski, Opial, Grüss, 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.

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.

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.

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.

This compact book focuses on self-adjoint operators' well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. 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.

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.

In this short monograph Newton-likeand other similar numerical methods with applications to solving multivariateequations are developed, which involve Caputotype fractional mixed partial derivatives and multivariate fractional Riemann-Liouvilleintegral operators.

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.

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.

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.

This book applies the free, downloadable SAGE software program to numerous of examples and solved as well as unsolved problems in linear algebra and differential geometry, offering plenty of SAGE applications at each stage of the exposition.

Statistical convergence has been explored in numerous contexts such as fuzzy logic theory. Here, the authors approach the subject by approximating a function by linear operators, focusing on situations in which the classical limit is not effective.

This book presents the Opial, Poincare, Sobolev, Hilbert and Ostrowski fractional differentiation equalities, and results are derived for each using three different types of fractional derivatives. The univariate and multivariate cases are both examined.

Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. This book examines a wide array of topics in computational analysis.

This book solves mathematical analysis problems using popular software packages. Besides fundamental theoretical notions, the book offers many exercises solved both mathematically and by computer, using Matlab 7.9, Mathcad 14, Mathematica 8 or Maple 15.

This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases.

Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory.

This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases.

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives.