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Approximation By Complex Bernstein And Convolution Type Operators

Name: Approximation By Complex Bernstein And Convolution Type Operators
Brand: World Scientific Publishing Co Pte Ltd
SKU: 05069834
Price: 139.59 EUR
Availability: InStock
Author: Sorin G. Gal
ISBN: 9789814282420

Sorin G. Gal

Language

English

Book Hardback

Libristo code: 05069834

Publishers World Scientific Publishing Co Pte Ltd, August 2009

This monograph, as its first main goal, aims to study the overconvergence phenomenon of important cl... Full description

Libristo code: 05069834

342 b

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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. The operators studied are of the following types: Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szasz-Mirakjan, Baskakov and Balazs-Szabados. The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallee Poussin, Fejer, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDE) also are presented. Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.