Approximation by Complex Bernstein and Convolution Type Operators: 8 (Series on Concrete & Applicable Mathematics) - Hardcover

Sorin G Gal

Hardcover

ISBN 10: 9814282421 ISBN 13: 9789814282420

Publisher: World Scientific Publishing, 2009

Synopsis

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, BernsteinFaber, BernsteinButzer, q-Bernstein, BernsteinStancu, BernsteinKantorovich, FavardSzászMirakjan, Baskakov and BalázsSzabados. 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, PoissonCauchy, GaussWeierstrass, q-Picard, q-GaussWeierstrass, PostWidder, 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.

About this title

From the Back Cover

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, BernsteinFaber, BernsteinButzer, q-Bernstein, BernsteinStancu, BernsteinKantorovich, FavardSzszMirakjan, Baskakov and BalzsSzabados.

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, PoissonCauchy, GaussWeierstrass, q-Picard, q-GaussWeierstrass, PostWidder, 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.

Edition details

• Publisher: World Scientific Publishing
• Publication date: 2009
• Language: English
• ISBN 10: 9814282421
• ISBN 13: 9789814282420
• Binding: Hardcover
• Number of pages: 352