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There are exponential operators which are defined on the whole real line, namely, the Ismail–May operators , connected to , and the Gauss–Weierstrass operators , connected with 1. Here we consider the composition of these two operators and observe that the composition operator is not of exponential type operator. We find moment‐generating functions and moments of these operators and estimate some point‐wise convergence of these operators using the characteristic function. We also estimate quantitative Voronovskaya type asymptotic formula and error estimation. Also, the difference of the composition operators with its components and is estimated in terms of modulus of continuity. Finally, we provide some graphs to see visualize the convergence by considering the function .
Vijay Gupta (Tue,) studied this question.