Ibragimov-Gadjiev operators based on q-integers

Abstract

In this paper, we define the q-analogue of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We study some approximation properties of these new operators, and we show that this sequence of operators is a generalization of well-known q-Bernstein, q-Chlodowsky, and q-Szasz-Mirakyan operators as a particular case.