Approximation by Max-Product Type Operators. 1st ed. 2016

種類:

電子ブック

責任表示:

by Barnabás Bede, Lucian Coroianu, Sorin G. Gal

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2016

著者名:

• Bede, Barnabás.
• Coroianu, Lucian.
• Gal, Sorin G.
• SpringerLink (Online service)

ISBN:

9783319341897 [3319341898]    

注記:

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.
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,

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