Rate of convergence by Jakimovski-Leviatan-Paltanea operators using generalized Brenke type polynomials

Abstract

In the present paper, we introduce a modification of Sz\'asz operators involving generalized Brenke type polynomials. First, we investigate Korovkin's type approximation theorem. Next, we established an approximation result for the functions in Lipschitz type space. Furthermore, we discuss the rate of convergence by means of the Ditzian-Totik modulus of smoothness. Lastly, we established an approximation result for the functions having derivatives of bounded variation.