Approximation properties of modified $q$-Gamma operators preserving linear functions

Abstract

In this paper, we introduce the $q$-analogue of modified Gamma operators preserving linear functions. We establish the moments of the operators using the $q$-Gamma functions. Next, some local approximation for the above operators are discussed. Also, the rate of
convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Furthermore, we obtain the Voronovskaja type theorem.