Some approximation results by (p, q)-analogue of Bernstein–Stancu operators

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In this paper, we introduce a new analogue of Bernstein–Stancu operators based on (p, q)-integers which we call as (p, q)-Bernstein–Stancu operators. We study approximation properties for these operators based on Korovkin’s type approximation theorem and also study some direct theorems. Furthermore, we give comparisons and some illustrative graphics for the convergence of operators to some function.

论文关键词:(p, q)-integers,Bernstein–Stancu operators,q-Bernstein–Stancu operators,Modulus of continuity,Positive linear operator,Korovkin’s type approximation theorem

论文评审过程:Received 24 December 2014, Revised 13 March 2015, Accepted 25 March 2015, Available online 20 May 2015, Version of Record 20 May 2015.

论文官网地址:https://doi.org/10.1016/j.amc.2015.03.135