Blending type approximation by generalized Szász type operators based on Charlier polynomials

Abstract

In the present paper, we introduce a generalized Szasz type operators based on ´ ρ(x) where ρ is a continuously differentiable function on [0, ∞), ρ(0) = 0 and inf ρ 0 (x) ≥ 1, x ∈ [0, ∞). This function not only characterizes the operators but also characterizes the Korovkin set 1, ρ, ρ2 in a weighted function space. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain a Voronovskaja type result and the rate of convergence in terms of the weighted modulus of continuity.