Modified Stancu operators based on inverse Polya Eggenberger distribution

Abstract

In this paper, we construct a sequence of modified Stancu-Baskakov operators for a real valued function bounded on [0, infinity), based on a function tau (x). This function tau (x) is infinite times continuously differentiable on [0, infinity) and satisfy the conditions tau (0) = 0, tau' (x) > 0 and tau '' (x) is bounded for all x epsilon [0, infinity). We study the degree of approximation of these operators by means of the Peetre K-functional and the Ditzian-Totik modulus of smoothness. The quantitative Voronovskaja-type theorems are also established in terms of the first order Ditzian-Totik modulus of smoothness.