Bernstein Operators and Their Properties

  • Jorge Bustamante

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jorge Bustamante
    Pages 1-73
  3. Jorge Bustamante
    Pages 75-160
  4. Jorge Bustamante
    Pages 161-173
  5. Jorge Bustamante
    Pages 175-271
  6. Jorge Bustamante
    Pages 273-294
  7. Jorge Bustamante
    Pages 295-347
  8. Jorge Bustamante
    Pages 359-369
  9. Jorge Bustamante
    Pages 371-395
  10. Jorge Bustamante
    Pages 397-399
  11. Back Matter
    Pages 401-420

About this book

Introduction

This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties.

This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter.

The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.

Keywords

Bernstein operators moduli of smoothness rate of approximation Bernstein inequality sub-additive majorants moments of operators semigroups of operators simultaneous approximation converse results Korovkin type theorems Voronovskaya type theorems approximation in Holder norms Besov spaces

Authors and affiliations

  • Jorge Bustamante
    • 1
  1. 1.Facultad de Ciencias Físico-MatemáticasBenemerita Universidad Autonoma de PueblaPueblaMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-55402-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-55401-3
  • Online ISBN 978-3-319-55402-0
  • About this book