Approximation by modified q-Gamma type operators via A-statistical convergence and power series method.

In this article, we introduce a q-analogue of the operators defined by Usta and Betus (Linear Multilinear Algebra, DOI: 10.1080/03081087.2020.1791033 (2020)) and find a general expression of moments for the q- operators. Next, we study the approximation properties of these operators in a weighted space via A-statistical method and the power series method. Later, we define a k-th order generalization of the q- operators by using the approach of Kirov and Popova (Math. Balk. 7, 149–162 (1993)) and estimate the error in the approximation for the C k functions in a Lipschitz class. We modify these operators so that they reproduce the constant as well as a monomial and provide better approximation. Finally, we introduce some graphical results to validate our theoretical claims. [ABSTRACT FROM AUTHOR]