Fuzzy mathematics : approximation theory

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Fuzzy mathematics : approximation theory / George A. Anastassiou

資料種別:: 図書
出版情報:: Berlin : Springer, c2010
形態:: xii, 443 p. ; 25 cm
シリーズ名:: Studies in fuzziness and soft computing ; 251 <BA28659077>
著者名:: Anastassiou, George A., 1952-
ISBN:: 9783642112195 [3642112196]
書誌ID:: BB01428627

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ISSN:

14349922

注記:

Includes bibliographical references and index

主題:

Approximation theory; Fuzzy mathematics

言語:

英語

目次情報:

Introduction / 1：

Basics / 1.1：

Background / 1.2：

Chapters description / 1.3：

About H-Fuzzy Differentiation / 2：

Basic Results / 2.1：

Main Results / 2.4：

On Fuzzy Taylor Formulae / 3：

Addendum / 3.1：

Fuzzy Ostrowski Inequalities / 4：

Results / 4.1：

A Fuzzy Trigonometric Approximation Theorem of Weierstrass-Type / 5：

Preliminaries / 5.1：

Main Result / 5.3：

General Remarks / 5.4：

On Best Approximation and Jackson-Type Estimates by Generalized Fuzzy Polynomials / 6：

Best approximation, trigonometric case / 6.1：

Best approximation, algebraic case / 6.3：

Application to fuzzy interpolation / 6.4：

Basic Fuzzy Korovkin Theory / 7：

Fuzzy Trigonometric Korovkin Theory / 7.1：

Fuzzy Global Smoothness Preservation / 8.1：

Fuzzy Korovkin Theory and Inequalities / 9.1：

Related Results / 10.1：

Higher Order Fuzzy Korovkin Theory Using Inequalities / 10.3：

Univariate Results / 11.1：

Multidimensional Results / 11.3：

L_p-estimates, p ≥ 1 / 11.4：

Applications / 11.5：

Fuzzy Wavelet Like Operators / 12：

Estimates To Distances between Fuzzy Wavelet like Operators / 12.1：

Fuzzy Approximation by Fuzzy Convolution Operators / 13.1：

Main results / 14.1：

Degree Of Approximation of Fuzzy Neural Network Operators, Univariate Case / 15：

Basic Properties / 15.1：

Higher Degree of Fuzzy Approximation by Fuzzy Wavelet Type and Neural Network Operators / 15.3：

Fuzzy Random Korovkin Theorems and In-Equalities / 16.1：

Auxilliary Material / 17.1：

Application / 17.3：

Fuzzy-Random Neural Network Approximation Operators, Univariate Case / 18：

Basic properties / 18.1：

X-Summability and Fuzzy Korovkin Approximation / 18.3：

A Fuzzy Korovkin Type Theorem / 19.1：

Rate of Convergence / 19.3：

A-Summability and Fuzzy Trigonometric Korovkin Approximation / 20：

Uniform Real and Fuzzy Estimates for Distances between Wavelet Type Operators at Real and Fuzzy Environment / 20.1：

Estimates for Distances of Real Wavelet type Operators / 21.1：

Estimates for Distances of Fuzzy Wavelet type Operators / 21.2：

References

List of Symbols

Index

Introduction / 1：

Basics / 1.1：

Background / 1.2：

Chapters description / 1.3：

About H-Fuzzy Differentiation / 2：

Basic Results / 2.1：

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