On Szász-Mirakyan-Jain Operators preserving exponential functions

Abstract

In the present work a Jain type modification of the generalized Szász-Mirakyan operators that preserve constant and exponential mappings is presented. The introduction of this operator helps to extend the class of operators that preserve exponential functions. A particular expansion involving the Lambert W-function is established which is used to obtain properties of the operator. Moments, and central moments, are presented with some limiting properties. A Voronovskaya type theorem, as well as other theorems, are discussed with results. Other select properties are also presented.Moments, recurrence formulas, and other identities are established for these operators. Approximation properties are also obtained with use of the Bohman-Korovkin theorem.