Jorge Bustamante Knihy

Focusing on the theory of approximation by algebraic polynomials, this book presents direct and converse theorems within a finite interval. It also addresses essential aspects of trigonometric approximation for context and comparison. The included selection of referenced papers highlights significant trends in polynomial approximation from the 1950s to the present, showcasing the evolution of the field and its foundational results.

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.