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© 2017

Approximation with Positive Linear Operators and Linear Combinations

Benefits

  • 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

Book

Part of the Developments in Mathematics book series (DEVM, volume 50)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Vijay Gupta, Gancho Tachev
    Pages 1-14
  3. Vijay Gupta, Gancho Tachev
    Pages 15-23
  4. Vijay Gupta, Gancho Tachev
    Pages 37-65
  5. Vijay Gupta, Gancho Tachev
    Pages 67-87
  6. Vijay Gupta, Gancho Tachev
    Pages 117-155
  7. Vijay Gupta, Gancho Tachev
    Pages 157-173
  8. Back Matter
    Pages 175-186

About this book

Introduction

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.  


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

Authors and affiliations

  1. 1.Department of MathematicsNetaji Subhas Institute of TechnologyNew DelhiIndia
  2. 2.Department of MathematicsUniversity of Architecture Civil Engineering and GeodesySofiaBulgaria

Bibliographic information

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)