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Bernstein Operators and Their Properties

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概要 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.
目次 Preface
Preliminaries
Basic properties of Bernstein operators
Bernstein polynomials as linear operators
Upper estimates of the error with Bernstein operators
Bernstein type inequalities
Converse results
Iterates of Bernstein polynomials
Linear combination of Bernstein polynomials
Final comments.
冊子版へのリンク
本文を見る Full text available from SpringerLINK ebooks - Mathematics and Statistics (2017)
Full text available from SpringerLink ebooks - Mathematics and Statistics without Lecture Notes (2017)

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登録日 2017.07.11
更新日 2017.12.27