q- Lupas Kantorovich operators based on Polya distribution

The purpose of the present paper is to introduce a Kantorovich modification of the q-analogue of the Stancu operators defined by Nowak (J Math Anal Appl 350:50–55, 2009). We study a local and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness. Further A-statistical convergence properties of these operators are investigated. Next, a bivariate generalization of these operators is introduced and its rate of convergence is discussed with the aid of the partial and complete modulus of continuity and the Peetre‘s K-functional. © 2017, Università degli Studi di Ferrara.