Approximation by Complex Bernstein and Convolution Type Operators (Concrete and Applicable Mathematics, Band 8) - Hardcover

Inhaltsangabe

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 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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.