Some approximation results by Bernstein-Kantorovich operators based on (p,q)-integers

2015/04/16 by M. Mursaleen, Mursaleen, M., Khursheed J‎. ‎Ansari +3
Computer Science · Decision Sciences · Mathematics · #40A30 #41A10 #41A25 #41A36 #Advanced Algebra and Logic #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1504.05887

openalex publication_date 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, First we have given the modified form of (p,q)-analogues of Bernstein and Bernstein operators [21-23] and then we introduce a new analogue of Bernstein-Kantorovich operators which we call as (p,q)-Bernstein-Kantorovich operators. 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 f is a Lipschitz function. Moreover, we also study the local approximation property of the (p,q)-Kantorovich operators . 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.

Citations

• On (p,q)-analogue of Bernstein Operators (Revised)
• On the fundamental theorem of (p,q)-calculus and some (p,q)-Taylor\n formulas

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