Direct Estimates for Lupas-Durrmeyer Operators

Abstract

The generalization of the Bernstein polynomials based on Polya distribution was first considered by Stancu [14]. Very recently Gupta and Rassias [6] proposed the Durrmeyer type modification of the Lupas, operators and established some results. Now we extend the studies and here we estimate the convergence estimates, which include quantitative asymptotic formula and rate of approximation bounded variation. We also give an open problem for readers to obtain the moments using hypergeometric function.