BETTER DEGREE OF APPROXIMATION BY MODIFIED BERNSTEIN-DURRMEYER TYPE OPERATORS

In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function tau(x), where tau is infinitely differentiable function on [0,1], tau(0) = 0, tau(1) = 1 and tau'(x) > 0, for all x is an element of [0, 1]. We study the degree of approximation by means of the modulus of continuity and the Ditzian-Totik modulus of smoothness. A Voronovskaja type asymptotic theorem and the approximation of functions with derivatives of bounded variation are also studied. By means of a numerical example, finally we illustrate the convergence of these operators to certain functions through graphs and show a careful choice of the function tau(x) leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [11].