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The convergence of (p,q)-Bernstein operators for the Cauchy kernel with a pole via divided difference
Journal article   Open access  Peer reviewed

The convergence of (p,q)-Bernstein operators for the Cauchy kernel with a pole via divided difference

Faisal Khan, Mohd Saif, Aiman Mukheimer and M. Mursaleen
Journal of inequalities and applications, Vol.2019(1), pp.1-11
14/05/2019
DOI: https://doi.org/10.1186/s13660-019-2090-y

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this paper, some qualitative approximation results for the (p, q)-Bernstein operators Bnp, q(f; x) are obtained for the Cauchy kernel 1 x-a with a pole a. [0, 1] for q > p > 1. The main focus lies in the study of behavior of operators Bnp, q(f; x) for the function fm(x) = 1 x-pmq-m, x = pmq-m and fm(pmq-m) = a, a. R and the extra parameter p provides flexibility for the approximation.
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https://doi.org/10.1186/s13660-019-2090-yView
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