Abstract
AbstractWe construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under a domain transformation, we analyze the bivariate Bernstein–Stancu operators, and we introduce Bernstein-type operators on disk quadrants by means of continuously differentiable transformations of the function. We state convergence results for continuous functions and we estimate the rate of convergence. Finally some interesting numerical examples are given, comparing approximations using the shifted Bernstein–Stancu and the Bernstein-type operator on disk quadrants.
Funder
Ministerio de Ciencia, Innovación y Universidades
Junta de Andalucía
Universidad de Granada
Publisher
Springer Science and Business Media LLC
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