SOME APPROXIMATION RESULTS FOR BERNSTEIN-KANTOROVICH OPERATORS BASED ON (p, q)-CALCULUS

作者：Mursaleen M; Ansari Khursheed J; Khan Asif

来源：Polytechnical University of Bucharest Scientific Bulletin Series A- Applied Mathematics and Physics, 2016, 78(4): 129-142.

• (p, q)-integers
• (p, q)-Bernstein-Kantorovich operators
• q-Bernstein-Kantorovich operators
• modulus of continuity
• positive linear operators
• Korovkin type approximation theorem

In this paper, a new analogue of Bernstein-Kantorovich operators as (p,q)-Bernstein-Kantorovich operators are introduced. We discuss approximation properties for these operators based on Korovkin's type approximation theorem and we compute the order of convergence using usual modulus of continuity and also the rate of convergence when the function f belongs to the class Lip(M) (alpha). Moreover, the local approximation property of the sequence of positive linear operators K-n((p,q)) has been studied. We show comparisons and some illustrative graphics for the convergence of operators to a function. In comparison to q-analogoue of Bernstein-Kantorovich operators, our generalization gives more flexibility for the convergence of operators to a function.

• 出版日期2016