Stancu-durrmeyer type operators based on q-integers

Abstract

In this paper, we construct the Stancu-Durrmeyer-type modification of q-Bernstein operators by means of q-Jackson integral. Here, we establish moment estimates and some direct results which include basic convergence theorem, local approximation theorem and approximation for a Lipschitz type space. Also, we establish the Korovkin type A-statistical approximation theorem and rates of A-statistical convergence in terms of the modulus of continuity. Mathematics Subject Classification(2010): 41A25, 26A15. © 2017. NSP Natural Sciences Publishing Cor.