Approximation by complex Bernstein and convolution type operators /

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The 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. T...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Gal, Sorin G., 1953-
Autor Corporativo: World Scientific (Firm)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2009.
Colección:Series on concrete and applicable mathematics ; v. 8.
Temas:
Approximation theory.
Operator theory.
Bernstein polynomials.
Convolutions (Mathematics)
Théorie de l'approximation.
Théorie des opérateurs.
Polynômes de Bernstein.
Convolutions (Mathématiques)
MATHEMATICS > General.
Approximation theory
Bernstein polynomials
Operator theory
Acceso en línea:Texto completo
Descripción
Sumario:The 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-Szász-Mirakjan, Baskakov and Balázs-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 Vallée Poussin, Fejér, 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 (PDEs) are also 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.
Descripción Física:1 online resource (xii, 337 pages)
Bibliografía:Includes bibliographical references (pages 327-336) and index.
ISBN:9789814282437
981428243X
ISSN:1793-1142 ;

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