Approximation properties of \((p,q)\)-Szász-Mirakjan-Durrmeyer operators (Q2024574)

Summary: In this article, we introduce a new Durrmeyer-type generalization of \((p,q)\)-Szász-Mirakjan operators using the \((p,q)\)-gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre \(\mathcal{K}\)-functional. Finally, the rate of convergence and weighted approximation of these operators are presented.