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Author Bede, Barnabas,
Title Approximation by max-product type operators / Barnabas Bede, Lucian Coroianu, Sorin G. Gal.
Imprint Switzerland : Springer, [2016]

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View online
Author Bede, Barnabas,
Subject Approximation theory.
Operator theory.
Constructive mathematics.
Fuzzy mathematics.
Alt Name Coroianu, Lucian,
Gal, Sorin G., 1953-
Description 1 online resource
polychrome rdacc
Bibliography Note Includes bibliographical references and index.
Contents Preface; Contents; 1 Introduction and Preliminaries; 1.1 Introduction; 1.1.1 Linear Approximation Operators; 1.1.2 Definitions of the Max-Product Operators; 1.1.3 Main Characteristics of the Max-Product Operators; 1.2 Preliminaries; 1.2.1 Notes on Fuzzy Numbers; 1.2.2 Notes on Possibility Theory; 2 Approximation by Max-Product Bernstein Operators; 2.1 Estimates for Positive Functions; 2.2 Improved Estimates for Strictly Positive Functions; 2.3 Saturation Results; 2.4 Localization Results; 2.5 Iterations and Fixed Points; 2.6 Applications to Approximation of Fuzzy Numbers.
2.6.1 Uniform Approximation and Preservation of Characteristics2.6.2 L1-Approximation; 2.7 Bivariate Max-Product Bernstein Operators; 2.8 Applications to Image Processing; 2.9 Notes; 3 Approximation by Max-Product Favard-Szasz-Mirakjan Operators; 3.1 Non-Truncated Operators; 3.2 Truncated Operators; 4 Approximation by Max-Product Baskakov Operators; 4.1 Non-Truncated Operators; 4.2 Truncated Operators; 5 Approximation by Max-Product Bleimann-Butzer-Hahn Operators; 5.1 Quantitative Estimates; 5.2 Shape Preserving Properties; 6 Approximation by Max-Product Meyer-Konig and Zeller Operators.
6.1 Estimates and Shape Preserving Properties6.2 Saturation Results; 6.3 Localization Results; 6.4 Note; 7 Approximation by Max-Product Interpolation Operators; 7.1 Max-Product Hermite-Fejer Interpolation on Chebyshev Knots; 7.2 Max-Product Lagrange Interpolation on Chebyshev Knots; 7.3 Modified Max-Product Lagrange Interpolation on General Knots; 7.4 Saturation Results for Equidistant Knots; 7.5 Localization Results for Equidistant Knots; 8 Approximations by Max-Product Sampling Operators; 8.1 Max-Product Generalized Sampling Operators.
8.2 Max-Product Sampling Operators Based on Sinc-Type Kernels8.3 Saturation and Localization for Truncated Operators; 8.3.1 The Saturation Order for the Tn(M) Operator; 8.3.2 The Saturation Order for the Wn(M) Operator; 8.3.3 Local Inverse Result for the Tn(M) Operator; 8.3.4 Localization and Local Direct Result for the Tn(M) Operator; 8.3.5 Localization, Local Inverse, and Local Direct Results for the Wn(M) Operator; 8.4 Saturation and Localization for Non-Truncated Operators; 8.4.1 Saturation for the Case of Fejer Kernel; 8.4.2 Local Inverse Result for the Case of Fejer Kernel.
8.4.3 Localization Results in the Case of Fejer Kernel8.4.4 The Case of the Whittaker operator; 8.5 Notes; 9 Global Smoothness Preservation Properties; 9.1 The Case of Max-Product Bernstein operator; 9.2 The Case of Max-Product Hermite-Fejer Operator; 9.3 The Case of Max-Product Lagrange Operator; 10 Possibilistic Approaches of the Max-Product Type Operators; 10.1 Bernstein-Type Approach in Possibility Theory; 10.1.1 Max-Product Operators on C+[0, 1]; 10.1.2 Max-Product Operators on UC+[0, +∞); 10.2 Feller's Scheme in Possibility Theory
Summary This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility. Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.
Note Online resource; title from PDF title page (EBSCO, viewed August 22, 2016).
ISBN 9783319341897 (electronic bk.)
3319341898 (electronic bk.)
OCLC # 956505364
Additional Format Erscheint auch als: Druck-Ausgabe Bede, Barnabas. Approximation by Max-Product Type Operators

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