Statistical convergence of q-analogue of Aldaz-Kounchev-Render operators

The prime purpose of this paper is to establish various approximation results of a q-analogue of Aldaz-Kounchev-Render (q-AKR) operators. Firstly, we obtain the central moments and estimate the convergence rate and Voronovskaja-type results for continuous functions via the modulus of continuity. Then, we provide the results on A-statistical convergence i.e. the Korovkin-type Theorem and the rate of A-statistical convergence of q-AKR operators. Finally, the rate of A-statistical convergence for Lipschitz-type functions is also discussed.