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Approximation by Max-Product Type Operators

  • Book
  • © 2016

Overview

Authors:
  1. Barnabás Bede

    1. Department of Mathematics, DigiPen Institute of Technology, Redmond, USA

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  2. Lucian Coroianu

    1. Dept. of Math. and Compt. Sci., University of Oradea, Oradea, Romania

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  3. Sorin G. Gal

    1. Dept. of Math. and Compt. Sci., University of Oradea, Oradea, Romania

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  • Presents a broad treatment of so-called "max-product" type operators
  • Discusses the analogy between the probabilistic and possibilistic approaches of the classical Bernstein type operators
  • Considers a wide variety of operators which are studied for a number of interesting problems
  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction and Preliminaries

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 1-24

  3. Approximation by Max-Product Bernstein Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 25-158

  4. Approximation by Max-Product Favard–Szász–Mirakjan Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 159-188

  5. Approximation by Max-Product Baskakov Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 189-228

  6. Approximation by Max-Product Bleimann–Butzer–Hahn Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 229-243

  7. Approximation by Max-Product Meyer–König and Zeller Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 245-279

  8. Approximation by Max-Product Interpolation Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 281-325

  9. Approximations by Max-Product Sampling Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 327-392

  10. Global Smoothness Preservation Properties

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 393-405

  11. Possibilistic Approaches of the Max-Product Type Operators

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 407-428

  12. Max-Product Weierstrass Type Functions

    • Barnabás Bede, Lucian Coroianu, Sorin G. Gal
    Pages 429-447

  13. Back Matter

    Pages 449-458
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Keywords

About this book

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 somefuzzy 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.

Reviews

“It is very well written and organized, with clear and simple proofs together with some new mathematical techniques. Therefore it can be recommended as a textbook for graduate students and postgraduate researchers as well as a reference book for researchers and professionals working not only in approximation theory, mathematical analysis, and numerical analysis, but also in signal theory, image processing, sampling theory, and engineering.” (Harun Karsli, Mathematical Reviews, 2018)

Authors and Affiliations

  • Department of Mathematics, DigiPen Institute of Technology, Redmond, USA

    Barnabás Bede

  • Dept. of Math. and Compt. Sci., University of Oradea, Oradea, Romania

    Lucian Coroianu, Sorin G. Gal

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