Approximation by Szasz-Mirakjan-Baskakov operators based on shape parameter

Abstract

In this In this paper, we aim to obtain several approximation properties of Szasz-Mirakjan-Baskakov operators with shape parameter lambda in [-1,1]. We reach some preliminary results such as moments and central moments. Next, we estimate the order of convergence with respect to the usual modulus of continuity, for the functions belong to Lipschitz-type class and Peetre's K-functional, respectively. Also, we prove a result concerning the weighted approximation for these operators. Finally, we give the comparison of the convergence of these newly defined operators to certain functions with some graphics.