โ Scribed by Barnabรกs Bede, Lucian Coroianu, Sorin G. Gal
No coin nor oath required. For personal study only.
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.
Front Matter....Pages i-xv
Introduction and Preliminaries....Pages 1-24
Approximation by Max-Product Bernstein Operators....Pages 25-158
Approximation by Max-Product FavardโSzรกszโMirakjan Operators....Pages 159-188
Approximation by Max-Product Baskakov Operators....Pages 189-228
Approximation by Max-Product BleimannโButzerโHahn Operators....Pages 229-243
Approximation by Max-Product MeyerโKรถnig and Zeller Operators....Pages 245-279
Approximation by Max-Product Interpolation Operators....Pages 281-325
Approximations by Max-Product Sampling Operators....Pages 327-392
Global Smoothness Preservation Properties....Pages 393-405
Possibilistic Approaches of the Max-Product Type Operators....Pages 407-428
Max-Product Weierstrass Type Functions....Pages 429-447
Back Matter....Pages 449-458
Approximation theory;Measure theory;Operator theory;Information theory;Mathematics
๐ SIMILAR VOLUMES
<p><p><p>This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases. It also explores approximations under convexity and a new trend in approximation theory โapproximation by sublinear operators with application
"This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases. It also explores approximations under convexity and a new trend in approximation theory -approximation by sublinear operators with applications to max
This monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals.
This monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals.
This monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals.