Approximation degree of Durrmeyer-Bezier type operators

Abstract

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szasz type operators, was introduced. In this paper, we study Bezier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means of the unified Ditzian-Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed.