George A. Anastassiou Ordine dei libri

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.

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.

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.

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.

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.

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.

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.

The book delves into approximation theory, emphasizing both ordinary and fractional smoothness in univariate and multivariate contexts. It introduces innovative concepts such as approximations under convexity and the use of sublinear operators, particularly for max-product operators, which offer rapid and adaptable solutions. The findings have significant implications across various fields of pure and applied mathematics, making it an essential resource for researchers, graduate students, and academic seminars in approximation theory and numerical analysis.

This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. 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.

Focusing on approximation theory, this monograph compiles the author's research over the past five years. Each chapter is self-contained, allowing for independent reading, and covers a range of diverse topics. The book serves as a resource for advanced courses, making it suitable for both students and educators in the field.