Overview

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-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 (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.

Full Product Details

Author:   Sorin G Gal (Univ Of Oradea, Romania)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   8
Dimensions:   Width: 16.80cm , Height: 2.50cm , Length: 24.90cm
Weight:   0.748kg
ISBN:  

9789814282420

ISBN 10:   9814282421
Pages:   352
Publication Date:   12 August 2009
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Bernstein-Type Operators of One Complex Variable: Auxiliary Results in Complex Analysis; Bernstein Polynomials; Iterates of Bernstein Polynomials; Generalized Voronovskaja Theorems for Bernstein Polynomials; Butzer's Linear Combination of Bernstein Polynomials; q-Bernstein Polynomials; Bernstein-Stancu Polynomials; Bernstein-Kantorovich Type Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Balazs-Szabados Operators; Bibliographical Notes and Open Problems; Bernstein-Type Operators of Several Complex Variables: Introduction; Bernstein Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Bibliographical Notes and Open Problems; Complex Convolutions: Linear Polynomial Convolutions; Linear Non-Polynomial Convolutions; Nonlinear Complex Convolutions; Bibliographical Notes and Open Problems; Appendices: Related Topics: Bernstein Polynomials of Quaternion Variable; Approximation of Vector-Valued Functions; Strong Approximation by Complex Taylor Series; Bibliographical Notes and Open Problems.

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