Properties of Convergence for a Class of Generalized $q$-Gamma Operators.

Abstract

In this paper, a generalization of $q$-Gamma operators based on the concept of $q$-integer is introduced. We investigate the moments and central moments of the operators by computation, obtain a local approximation theorem and get the pointwise convergence rate theorem and also obtain a weighted approximation theorem. Finally, a Voronovskaya type asymptotic formula was given.