Approximation by Max-Product Type Operators

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Approximation by Max-Product Type Operators

フォーマット:
電子ブック
責任表示:
by Barnabás Bede, Lucian Coroianu, Sorin G. Gal
本文言語:
英語
出版情報:
Cham, Germany. 2016-. Springer International Publishing,Imprint: Springer
概要:
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. 続きを見る
目次:
Preface
1. Introduction and Preliminaries
2. Approximation by Max-Product Bernstein Operators
3. Approximation by Max-Product Favard-Szász-Mirakjan Operators
4. Approximation by Max-Product Baskakov Operators
5. Approximation by Max-Product Bleimann-Butzer-Hahn Operators
6. Approximation by Max-Product Meyer-König and Zeller Operators
7. Approximation by Max-Product Interpolation Operators
8. Approximations by Max-Product Sampling Operators
9. Global Smoothness Preservation Properties
10. Possibilistic Approaches of the Max-Product Type Operators
11. Max-Product Weierstrass Type Functions
References
Index.
Preface
1. Introduction and Preliminaries
2. Approximation by Max-Product Bernstein Operators
3. Approximation by Max-Product Favard-Szász-Mirakjan Operators
4. Approximation by Max-Product Baskakov Operators
5. Approximation by Max-Product Bleimann-Butzer-Hahn Operators
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