On the preservation of functions with exponential growth by modified Ismail-May operators

摘要

In this study, our aim is to provide a modification of the so-called Ismail-May operators that preserve exponential functions eAx,A is an element of Double-struck capital R. In support of this, we begin by estimating the convergence rate of the operators in terms of usual and exponential modulus of continuity. We also provide a global approximation and a quantitative Voronovskaya result. Moreover, to validate the modification, we exhibit some graphical representations using Mathematica software to compare the original operator and its modification. We conclude that the modified operators not only preserve exponential functions but also provide faster rate of convergence for A > 0.