Approximation Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

Abstract

In this article, we introduce a new Durrmeyer-type generalization of $\left(p,q\right)$ -Szász-Mirakjan operators using the $\left(p,q\right)$ -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.