For the qualitative results of pointwise and uniform approximation obtained in [10], we present general quantitative estimates in terms of the modulus of continuity and in terms of a K-functional, for the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x , written in terms of the Choquet integral with respect to a family of monotone and submodular set functions, Γn,x, on the standar...

A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms andwhose eigenfunctions are orthogonal polynomialswith respect to Jacobiweights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein– Durrmeyer operators and orthogonal projections on polynomial subspaces. The quasi-interpolants satisfy...

In this paper, we construct a form of linear positive operators with Brenke type polynomials as a generalization of Szasz-Durrmeyer operators. We obtain convergence properties of our operators with the help of the universal Korovkin-type property and calculate the order of approximation by using classical modulus of continuity. Explicit examples of our operators involving some orthonogal and d-...

The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012). We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with...

This research paper is an introduction to a new type of analogue named as -analogue for well-known Baskakov Durrmeyer operators. considered reverse order -analogue. In this paper, we establish the direct approximation theorem, weighted theorem followed by estimations rate convergence these operators functions polynomial growth on interval.