Abstract
The purpose of this paper is to introduce a family of q-Szasz-Mirakjan-Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well-known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q-Szasz-Mirakjan-Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright (c) 2017 John Wiley & Sons, Ltd.