Bernstein Operators and Their Properties - Jorge Bustamante

Bernstein Operators and Their Properties

Buch | Softcover
XII, 420 Seiten
2018 | 1. Softcover reprint of the original 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-85651-3 (ISBN)
117,69 inkl. MwSt

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.

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.

"The book provides many useful historical details. Exercises are included at the end of each chapter. Detailed references are given when proofs are not included. This book is a valuable addition to the rich literature devoted to Bernstein operators. Useful for advanced graduate students and for researchers, it will stimulate further research in this area." (loan Rasa, Mathematical Reviews, November, 2017)

“The book provides many useful historical details. Exercises are included at the end of each chapter. Detailed references are given when proofs are not included. This book is a valuable addition to the rich literature devoted to Bernstein operators. Useful for advanced graduate students and for researchers, it will stimulate further research in this area.” (loan Raşa, Mathematical Reviews, November, 2017)

Erscheinungsdatum
Zusatzinfo XII, 420 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 6496 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte approximation in Holder norms • Bernstein inequality • Bernstein operators • Besov spaces • converse results • Korovkin type theorems • moduli of smoothness • moments of operators • rate of approximation • Semigroups of operators • simultaneous approximation • sub-additive majorants • Voronovskaya type theorems
ISBN-10 3-319-85651-0 / 3319856510
ISBN-13 978-3-319-85651-3 / 9783319856513
Zustand Neuware
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