Properties of Convergence for a Class of Generalized $q$-Gamma Operators. (Journal of Mathematical Study, 2021)
In this paper, a generalization of $q$-Gamma operators based on the conceptof $q$-integer is introduced. We investigate the moments and central moments of theoperators by computation, obtain a local approximation theorem and get the pointwiseconvergence rate theorem and also obtain a weighted approximation theorem. Finally,a Voronovskaya type asymptotic formula was given.
Keywords: $q$-integer; $q$-Gamma operators; weighted approximation; modulus of continuity.