This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.

This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.

Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results

This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.

This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.

This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators. It will be of interest to students both graduate and undergraduate studying linear positive operators and the area of approximation theory.

This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.

This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.

This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.

This book emphasizes some basic results in functional and classical analysis, including Hahn-Banach-type theorems, the Markov moment problem, polynomial approximation on unbounded subsets, convexity and convex optimization, elements of operator theory, a global method for convex monotone operators and a connection with the contraction principle. It points out the connection between linear continuous operators and convex continuous operators, and establishes their relationships with other fields of mathematics and physics. The book will appeal to students, PhD aspirants, researchers, professors, engineers, and any reader interested in mathematical analysis or its applications.