Title: APPROXIMATION BY COMPLEX BERNSTEIN AND CONVOLUTION TYPE OPERATORS (Concrete and Applicable Mathematics)
Publisher: World Scientific Publishing Company
Publication Date: 2009
Language: English
ISBN 10: 9814282421
ISBN 13: 9789814282420
Binding: Hardcover
Condition: New

About this title

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, Bernstein--Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Sz�sz-Mirakjan, Baskakov and Bal�zs-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 Vall�e Poussin, Fej�r, 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.

From the Back Cover

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.

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