George A. Anastassiou Libros

The book explores innovative activation functions in neural networks, emphasizing parametrized and deformed functions that retain more neurons compared to traditional methods. It highlights the brain's asymmetry through these deformed functions and introduces a wide range of general activation functions. The author's original work covers various neural network types, including ordinary, fractional, fuzzy, and stochastic approximations, as well as univariate and multivariate methods. Additionally, it examines iterated sequential multi-layer approximations within the context of Banach space-valued functions.

The book explores advanced concepts in fractional calculus, focusing on generalized methods of Hilfer, Prabhakar, and their combinations. It presents unifying fractional integral inequalities across various types, including Iyengar and Hardy, applicable in both univariate and multivariate contexts. The findings are poised for use in pure and applied mathematics, particularly in fractional inequalities and differential equations, with potential applications in fields like geophysics, chemistry, and engineering. It serves as a valuable resource for researchers, graduate students, and academic libraries.

The book explores the innovative impact of new trigonometric and hyperbolic Taylor's formulas with integral remainders, offering a comprehensive collection of approximations. It delves into perturbed neural network approximations, their links to Brownian motion, and various analytical inequalities. Covering both univariate and multivariate cases, it addresses Korovkin theory and singular integrals. The findings have broad applications across mathematics, computer science, engineering, and artificial intelligence, making it a vital resource for researchers and students in related fields.

Focusing on abstract kernel fractional calculus, this book explores both univariate and bivariate applications, including monotone approximation using polynomials and splines. It delves into constrained approximations with pseudo-polynomials, aiming to bridge theoretical concepts with practical applications in fields such as geophysics, physics, chemistry, economics, and engineering. Designed for researchers, graduate students, and practitioners, it serves as a valuable resource for those interested in fractional approximation and differential equations.

Focusing on computational and fractional analysis, this book delves into key inequalities such as the Iyengar type and Choquet integral analytical inequalities, essential for economic applications. It explores local fractional derivatives of Riemann-Liouville type, low order derivatives, and related approximations. The text also addresses quantitative complex approximation theory and important complex fractional inequalities, including conformable fractional approximations. Additionally, it introduces new local fractional M-derivatives and presents a complex multivariate Taylor formula, making it a valuable resource for researchers and graduate students in mathematics.

Focusing on constructive approximation theory, this work explores ordinary and fractional approximations through various operators and singular integrals. It emphasizes original research on generalized fractional differentiation techniques and their applications to inequalities, including Opial and Hardy types. The book also covers fractional Landau inequalities and multivariate fractional Taylor formulae. Aimed at researchers and graduate students, it highlights the growing significance of fractional analysis in mathematics and its real-world applications, making it a valuable resource for academic libraries.

The book explores advanced inequalities in the context of fractional calculus, specifically focusing on generalized Caputo fractional Ostrowski and Grüss-type inequalities for Banach algebra valued functions. It introduces various refined inequalities and applies p-Schatten norms to derive significant results. The findings have broad applications in both pure and applied mathematics, particularly in fractional inequalities and differential equations, as well as in fields such as geophysics, physics, and engineering. It's a valuable resource for researchers and students in these disciplines.