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Approximation by max-product type operators

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Approximation by max-product type operators/ by Barnabas Bede, Lucian Coroianu, Sorin G. Gal.
作者:	Bede, Barnabas.
其他作者:	Coroianu, Lucian.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xv, 458 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Approximation theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-34189-7
ISBN:	9783319341897

Approximation by max-product type operators
Bede, Barnabas.

Approximation by max-product type operators[electronic resource] /by Barnabas Bede, Lucian Coroianu, Sorin G. Gal. - Cham :Springer International Publishing :2016. - xv, 458 p. :ill., digital ;24 cm.

Preface -- 1. Introduction and Preliminaries -- 2. Approximation by Max-Product Bernstein Operators -- 3. Approximation by Max-Product Favard-Szasz-Mirakjan Operators -- 4. Approximation by Max-Product Baskakov Operators -- 5. Approximation by Max-Product Bleimann-Butzer-Hahn Operators -- 6. Approximation by Max-Product Meyer-Konig 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.

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.

ISBN: 9783319341897

Standard No.: 10.1007/978-3-319-34189-7doiSubjects--Topical Terms:

527707
Approximation theory.

LC Class. No.: QA221

Dewey Class. No.: 511.4

Approximation by max-product type operators
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505 0 $a Preface -- 1. Introduction and Preliminaries -- 2. Approximation by Max-Product Bernstein Operators -- 3. Approximation by Max-Product Favard-Szasz-Mirakjan Operators -- 4. Approximation by Max-Product Baskakov Operators -- 5. Approximation by Max-Product Bleimann-Butzer-Hahn Operators -- 6. Approximation by Max-Product Meyer-Konig 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.
520 $a 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.
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