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Approximation by Max-Product Type Operators

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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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Series Title

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Call Number

004. BED a

Publisher

Cham, Switzerland : Springer Cham., 2016

Collation

XV, 458

Language

English

ISBN/ISSN

978-3-319-34189-7

Classification

004.

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

Operator Theory
Information and Communication

Specific Detail Info

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Statement of Responsibility

Barnabás Bede, Lucian Coroianu, Sorin G. Gal

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Cataloger

umi

Source

https://link.springer.com/book/10.1007/978-3-319-34189-7

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