Intelligent Systems Reference Library

Towards Intelligent Modeling: Statistical Approximation Theory

Authors: Anastassiou, George A., Duman, Oktay

  • First monograph in Statistical Approximation Theory and Fuzziness
  • Self-contained book including a lot of applications within the framework of Statistical Approximation as well as a complete list of references
  • Written by leading experts in the field
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  • ISBN 978-3-642-19826-7
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Hardcover $179.00
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valid through November 5, 2017
  • ISBN 978-3-642-19825-0
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Softcover $179.00
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  • ISBN 978-3-642-26817-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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 fuzzy-valued 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 complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained 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 self-contained 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

    Anastassiou, George A. (et al.)

    Pages 1-8

  • Statistical Approximation by Bivariate Picard Singular Integral Operators

    Anastassiou, George A. (et al.)

    Pages 9-23

  • Uniform Approximation in Statistical Sense by Bivariate Gauss-Weierstrass Singular Integral Operators

    Anastassiou, George A. (et al.)

    Pages 25-38

  • Statistical Lp-Convergence of Bivariate Smooth Picard Singular Integral Operators

    Anastassiou, George A. (et al.)

    Pages 39-60

  • Statistical Lp-Approximation by Bivariate Gauss-Weierstrass Singular Integral Operators

    Anastassiou, George A. (et al.)

    Pages 61-83

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-642-19826-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
valid through November 5, 2017
  • ISBN 978-3-642-19825-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
valid through November 5, 2017
  • ISBN 978-3-642-26817-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Towards Intelligent Modeling: Statistical Approximation Theory
Authors
Series Title
Intelligent Systems Reference Library
Series Volume
14
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Berlin Heidelberg
eBook ISBN
978-3-642-19826-7
DOI
10.1007/978-3-642-19826-7
Hardcover ISBN
978-3-642-19825-0
Softcover ISBN
978-3-642-26817-5
Series ISSN
1868-4394
Edition Number
1
Number of Pages
XVI, 236
Topics