On the Generalized Szasz-Mirakyan Operators

Abstract

In this paper, we construct sequences of Szasz-Mirakyan operators which are based on a function.. This function not only characterizes the operators but also characterizes the Korovkin set {1, rho, rho(2)} in a weighted function space. We give theorems about convergence of these operators to the identity operator on weighted spaces which are constructed using the function rho and which are subspaces of the space of continuous functions on R+. We give quantitative type theorems in order to obtain the degree of weighted convergence with the help of a weighted modulus of continuity constructed using the function rho Further, we prove some shape-preserving properties of the operators such as the rho-convexity and the monotonicity. Our results generalize the corresponding ones for the classical Szasz operators.