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Towards Intelligent Modeling: Statistical Approximation Theory

  • George A. Anastassiou
  • Oktay Duman

Part of the Intelligent Systems Reference Library book series (ISRL, volume 14)

Table of contents

  1. Front Matter
  2. George A. Anastassiou, Oktay Duman
    Pages 1-8
  3. George A. Anastassiou, Oktay Duman
    Pages 85-96
  4. George A. Anastassiou, Oktay Duman
    Pages 97-107
  5. George A. Anastassiou, Oktay Duman
    Pages 131-142
  6. George A. Anastassiou, Oktay Duman
    Pages 143-155
  7. George A. Anastassiou, Oktay Duman
    Pages 169-180
  8. George A. Anastassiou, Oktay Duman
    Pages 181-188
  9. George A. Anastassiou, Oktay Duman
    Pages 189-197
  10. George A. Anastassiou, Oktay Duman
    Pages 199-206
  11. George A. Anastassiou, Oktay Duman
    Pages 207-215
  12. Back Matter

About this book

Introduction

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.

Keywords

Intelligent Modeling Intelligent Systems Statistical Approximation Theory

Authors and affiliations

  • George A. Anastassiou
    • 1
  • Oktay Duman
    • 2
  1. 1.Department of Mathematical SciencesThe University of MemphisMemphisUSA
  2. 2.Department of MathematicsTOBB Economics and Technology UniversitySögütözüTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-19826-7
  • Copyright Information Springer Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-19825-0
  • Online ISBN 978-3-642-19826-7
  • Series Print ISSN 1868-4394
  • Series Online ISSN 1868-4408
  • Buy this book on publisher's site