Approximation Properties for Stancu Type q−Baskakov- Kantorovich Operators

Abstract

In recent years, due to the intensive development of q− calculus, generalizations of some operators related to q− calculus have emerged (see [2, 3, 7, 12–16]). Aral and Gupta defined q− generalization of the Baskakov operator and investigated approximation properties of these operators in [3]. In [13], Gupta and Radu introduced the BaskakovKantorovich operators based on q−integers and investigated their weighted statistical approximation properties. They also proved some direct estimations for error using weighted modulus of smoothness in case 0 < q < 1. In recent study Buyukyazici and Atakut [7] introduced a new Stancu type generalization of q− Baskakov operator is defined as