On Composition of Certain Exponential Operators

Abstract

In the present article, we deal with a class of exponential operators associated with $p(t)= t^r,\: t\in [0,\infty), \;1<r<2.$ We consider their composition with the well-known Sz\'{a}sz-Mirakjan operators and investigate the order of approximation using Taylor's formula. We further discuss the approximation properties of the composition operators by employing the modulus of smoothness and Peetre's K-function. Moreover, Voronovskaja-type asymptotic theorems are given. Additionally, we provide further compositions and compare their approximation properties graphically.