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Fuzzy Mathematics: Approximation Theory

  • Book
  • © 2010

Overview

Authors:
  1. George A. Anastassiou

    1. Department of Mathematical Sciences, The University of Memphis, 38152, USA

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  • Introductory book to Fuzzy Mathematics
  • The State of the art of Approximation theory and Fuzzy Mathematics

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 251)

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Table of contents (21 chapters)

  1. Front Matter

    Download chapter PDF

  2. INTRODUCTION

    • George A. Anastassiou
    Pages 1-14

  3. ABOUT H-FUZZY DIFFERENTIATION

    • George A. Anastassiou
    Pages 15-50

  4. ON FUZZY TAYLOR FORMULAE

    • George A. Anastassiou
    Pages 51-63

  5. FUZZY OSTROWSKI INEQUALITIES

    • George A. Anastassiou
    Pages 65-73

  6. A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE

    • George A. Anastassiou
    Pages 75-82

  7. ON BEST APPROXIMATION AND JACKSON-TYPE ESTIMATES BY GENERALIZED FUZZY POLYNOMIALS

    • George A. Anastassiou
    Pages 83-97

  8. BASIC FUZZY KOROVKIN THEORY

    • George A. Anastassiou
    Pages 99-104

  9. FUZZY TRIGONOMETRIC KOROVKIN THEORY

    • George A. Anastassiou
    Pages 105-113

  10. FUZZY GLOBAL SMOOTHNESS PRESERVATION

    • George A. Anastassiou
    Pages 115-124

  11. FUZZY KOROVKIN THEORY AND INEQUALITIES

    • George A. Anastassiou
    Pages 125-157

  12. HIGHER ORDER FUZZY KOROVKIN THEORY USING INEQUALITIES

    • George A. Anastassiou
    Pages 159-190

  13. FUZZY WAVELET LIKE OPERATORS

    • George A. Anastassiou
    Pages 191-207

  14. ESTIMATES TO DISTANCES BETWEEN FUZZY WAVELET LIKE OPERATORS

    • George A. Anastassiou
    Pages 209-236

  15. FUZZY APPROXIMATION BY FUZZY CONVOLUTION OPERATORS

    • George A. Anastassiou
    Pages 237-261

  16. DEGREE OF APPROXIMATION OF FUZZY NEURAL NETWORK OPERATORS, UNIVARIATE CASE

    • George A. Anastassiou
    Pages 263-288

  17. HIGHER DEGREE OF FUZZY APPROXIMATION BY FUZZY WAVELET TYPE AND NEURAL NETWORK OPERATORS

    • George A. Anastassiou
    Pages 289-308

  18. FUZZY RANDOM KOROVKIN THEOREMS AND INEQUALITIES

    • George A. Anastassiou
    Pages 309-345

  19. FUZZY-RANDOM NEURAL NETWORK APPROXIMATION OPERATORS, UNIVARIATE CASE

    • George A. Anastassiou
    Pages 347-372

  20. \(\mathcal A\)-SUMMABILITY AND FUZZY KOROVKIN APPROXIMATION

    • George A. Anastassiou
    Pages 373-384
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Keywords

About this book

This monograph is the r st in Fuzzy Approximation Theory. It contains mostly the author s research work on fuzziness of the last ten years and relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to the broader area of Fuzzy Mathematics. Chapters are self-contained and several advanced courses can be taught out of this book. We provide lots of applications but always within the framework of Fuzzy Mathematics. In each chapter is given background and motivations. A c- plete list of references is provided at the end. The topics covered are very diverse. In Chapter 1 we give an extensive basic background on Fuzziness and Fuzzy Real Analysis, as well a complete description of the book. In the following Chapters 2,3 we cover in deep Fuzzy Di?erentiation and Integ- tion Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4 on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results on classical algebraic and trigonometric polynomial Fuzzy Approximation.

Authors and Affiliations

  • Department of Mathematical Sciences, The University of Memphis, 38152, USA

    George A. Anastassiou

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