Overview
- Overviews approximation by linear combinations of positive linear operators
- Enriches understanding of fundamental and recent results from the past decade
- Serves as a reference for graduate courses and a basis for future study and development
- Includes supplementary material: sn.pub/extras
Part of the book series: Developments in Mathematics (DEVM, volume 50)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
- positive linear operators
- Kantorovich Variants
- Discretely Dened Operators
- Approximation by Linear Combinations
- direct estimates
- inverse estimates
- Voronovskaja's Type Estimates
- Pointwise Estimates for Linear Combinations
- approximation of functions
- Szasz-Mirakjan-Baskakov Operators
- Durrmeyer type Operators
About this book
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 graduateand postgraduate courses as well as a basis for future study and development.
Reviews
“This book deals with linear positive operators, one of the central branches of approximation theory, and their combinations, which allows one to increase the degree of approximation. … It is carefully written and organized. In each chapter, remarkable comments and explanatory remarks are expressed that support and extend the basic text. … This significant book can be recommended as a source book to graduate students and researchers in approximation theory.” (Nurhayat İspır, Mathematical Reviews, January, 2018)
“The book under review written by two experts in approximation by positive linear operators (PLO, shortly), consists in eight chapters and contains most of the recent results in the topics announced by the contents of the book, very many belonging to the authors. … This book will be of interest to researchers working in approximation theory and for courses in approximation theory for graduate students.” (Sorin Gheorghe Ga, zbMATH 1371.41035, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Approximation with Positive Linear Operators and Linear Combinations
Authors: Vijay Gupta, Gancho Tachev
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-319-58795-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-58794-3Published: 07 July 2017
Softcover ISBN: 978-3-319-86476-1Published: 02 August 2018
eBook ISBN: 978-3-319-58795-0Published: 27 June 2017
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XIII, 186
Number of Illustrations: 2 illustrations in colour
Topics: Approximations and Expansions, Numerical Analysis, Functional Analysis