Approximation Properties of λ-Gamma Operators Based on q-Integers

Abstract

In the present paper, we will introduce λ-Gamma operators based on q-integers. First, the auxiliary results about the moments are presented, and the central moments of these operators are also estimated. Then, we discuss some local approximation properties of these operators by means of modulus of continuity and Peetre K-functional. And the rate of convergence and weighted approximation for these operators are researched. Furthermore, we investigate the Voronovskaja type theorems including the quantitative q-Voronovskaja type theorem and q-Grüss-Voronovskaja theorem.