Inequalities for a class of multivariate operators
Department of Mathematics, China Jiliang University, Hangzhou, 310018, P.R. China
Journal of Inequalities and Applications 2012, 2012:175 doi:10.1186/1029-242X-2012-175Published: 7 August 2012
This paper introduces and studies a class of generalized multivariate Bernstein operators defined on the simplex. By means of the modulus of continuity and so-called Ditzian-Totik’s modulus of function, the direct and inverse inequalities for the operators approximating multivariate continuous functions are simultaneously established. From these inequalities, the characterization of approximation of the operators follows. The obtained results include the corresponding ones of the classical Bernstein operators.
MSC: 41A25, 41A36, 41A60, 41A63.