Towards Intelligent Modeling: Statistical Approximation Theory
Authors: Anastassiou, George A., Duman, Oktay
Free Preview First monograph in Statistical Approximation Theory and Fuzziness
 Selfcontained book including a lot of applications within the framework of Statistical Approximation as well as a complete list of references
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 About this book

The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzyvalued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complexvalued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are selfcontained and several advanced courses can be taught.
The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
 Reviews

From the reviews:
“This is the first monograph in statistical approximation theory and fuzziness, which contains mostly the recent joint works of the authors … . The book consists of eighteen chapters which are selfcontained and include many significant applications. … A complete list of references and a useful index are presented at the end of the book. This monograph is recommended to graduate students and researchers, in both pure and applied mathematics, specializing in summability and approximation theories.” (Cihan Orhan, Mathematical Reviews, Issue 2012 k)
 Table of contents (18 chapters)


Introduction
Pages 18

Statistical Approximation by Bivariate Picard Singular Integral Operators
Pages 923

Uniform Approximation in Statistical Sense by Bivariate GaussWeierstrass Singular Integral Operators
Pages 2538

Statistical L p Convergence of Bivariate Smooth Picard Singular Integral Operators
Pages 3960

Statistical L p Approximation by Bivariate GaussWeierstrass Singular Integral Operators
Pages 6183

Table of contents (18 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Towards Intelligent Modeling: Statistical Approximation Theory
 Authors

 George A. Anastassiou
 Oktay Duman
 Series Title
 Intelligent Systems Reference Library
 Series Volume
 14
 Copyright
 2011
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 Springer Berlin Heidelberg
 eBook ISBN
 9783642198267
 DOI
 10.1007/9783642198267
 Hardcover ISBN
 9783642198250
 Softcover ISBN
 9783642268175
 Series ISSN
 18684394
 Edition Number
 1
 Number of Pages
 XVI, 236
 Topics