On Modification of Certain Exponential Type Operators Preserving Constant and $$e^{-x}$$

Abstract

The key goal of this article is to propose a modification of certain exponential type operators defined by Ismail and May. Particularly, we concentrate on a sequence of operators that preserve $$e^{-x}$$ and constant functions. We find the moments of these modified operators using the concept of moment generating function with the help of Mathematica software. We show uniform convergence of these modified operators and analyze the asymptotic behaviour with a Voronovskaya type theorem. We also illustrate via graphs that our modified operators approximate better than the original operators for certain family of functions. Finally, we show the convergence of these modified operators graphically using Mathematica Software.