Bézier Variant of Modified Srivastava–gupta Operators

Srivastava and Gupta proposed in 2003 a general family of linear positive operators which include several well known operators as its special cases and investigated the rate of convergence of these operators for functions of bounded variation by using the decomposition techniques. Subsequently, researchers proposed several modifications of these operators and studied their various approximation properties. Yadav, in 2014, proposed a modification of these operators and studied a Voronovskaya-type approximation theorem and statistical convergence. In this paper, we introduce the Bézier variant of the operators defined by Yadav and give a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation. Furthermore, we show the comparisons of the rate of convergence of the Srivastava–Gupta operators vis-à-vis its Bézier variant to a certain function by illustrative graphics using Maple algorithms.