Limit Theorems for Iterates of the Szász–Mirakyan Operator in Probabilistic View

The Szász–Mirakyan operator is known as a positive linear which uniformly approximates certain class of continuous functions on the half line. purpose present paper to find out limiting behaviors iterates in probabilistic point view. We show that converge semigroup generated by second-order degenerate differential operator. A interpretation convergence terms discrete Markov chain constructed from and diffusion process line captured well.