Bernstein Operators and Their Properties [Hardcover]

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 Ra_a, Mathematical Reviews, November, 2017)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. l£®