Approximation by Max-Product Type Operators

  • Barnabás Bede
  • Lucian Coroianu
  • Sorin G. Gal

Table of contents

  1. Front Matter
    Pages i-xv
  2. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 1-24
  3. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 25-158
  4. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 159-188
  5. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 189-228
  6. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 229-243
  7. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 245-279
  8. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 281-325
  9. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 327-392
  10. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 393-405
  11. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 407-428
  12. Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 429-447
  13. Back Matter
    Pages 449-458

About this book

Introduction

This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. 

Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility.

Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.

Keywords

interpolation operators Weierstrass type functions Baskakov operator Bleimann-Butzer-Hahn operator Bernstein operator max-product approximation max-product max-type operator constructive approximation possibilistic distribution

Authors and affiliations

  • Barnabás Bede
    • 1
  • Lucian Coroianu
    • 2
  • Sorin G. Gal
    • 3
  1. 1.Department of MathematicsDigiPen Institute of TechnologyRedmondUSA
  2. 2.Dept. of Math. and Compt. Sci.University of OradeaOradeaRomania
  3. 3.Dept. of Math. and Compt. Sci.University of OradeaOradeaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-34189-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-34188-0
  • Online ISBN 978-3-319-34189-7
  • About this book