DIRECT ESTIMATES FOR LUPAS-DURRMEYER OPERATORS

Abstract

The generalization of the Bernstein polynomials based on Polya distribution
was rst considered by Stancu [12]. Very recently Gupta and Rassias [4] proposed the
Durrmeyer type modication 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