Approximation Theory Using Positive Linear Operators

  • Radu Păltănea

Table of contents

  1. Front Matter
    Pages i-ix
  2. Radu Păltănea
    Pages 1-14
  3. Radu Păltănea
    Pages 15-68
  4. Radu Păltănea
    Pages 69-87
  5. Radu Păltănea
    Pages 89-129
  6. Radu Păltănea
    Pages 131-159
  7. Back Matter
    Pages 195-202

About this book


This work treats quantitative aspects of the approximation of functions using positive linear operators. The theory of these operators has been an important area of research in the last few decades, particularly as it affects computer-aided geometric design. In this book, the crucial role of the second order moduli of continuity in the study of such operators is emphasized. New and efficient methods, applicable to general operators and to diverse concrete moduli, are presented. The advantages of these methods consist in obtaining improved and even optimal estimates, as well as in broadening the applicability of the results.

Additional Topics and Features:

*  Examination of the multivariate approximation case

*  Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators

*  Many general estimates, leaving room for future applications (e.g. the B-spline case)

*  Extensions to approximation operators acting on spaces of vector functions

*  Historical perspective in the form of previous significant results

This monograph will be of interest to those working in the field of approximation or functional analysis. Requiring only familiarity with the basics of approximation theory, the book may serve as a good supplementary text for courses in approximation theory, or as a reference text on the subject.


Area Smooth function addition approximation approximation theory computer constant design field form function functional functional analysis functions types

Authors and affiliations

  • Radu Păltănea
    • 1
  1. 1.Department of MathematicsTransilvania UniversityBraşovRomania

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2004
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-4350-8
  • Online ISBN 978-1-4612-2058-9
  • Buy this book on publisher's site