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Symmetry 2018, 10(12), 731; https://doi.org/10.3390/sym10120731 (registering DOI)

On Some Statistical Approximation by (p,q)-Bleimann, Butzer and Hahn Operators

1
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
3
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
4
Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
*
Author to whom correspondence should be addressed.
Received: 29 October 2018 / Revised: 29 November 2018 / Accepted: 4 December 2018 / Published: 7 December 2018
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
PDF [310 KB, uploaded 7 December 2018]

Abstract

In this article, we propose a different generalization of ( p , q ) -BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where ( p , q ) -integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators.
Keywords: q–Bleimann–Butzer–Hahn operators; (p,q)-integers; (p,q)-Bernstein operators; (p,q)-Bleimann–Butzer–Hahn operators; modulus of continuity; rate of approximation; K-functional q–Bleimann–Butzer–Hahn operators; (p,q)-integers; (p,q)-Bernstein operators; (p,q)-Bleimann–Butzer–Hahn operators; modulus of continuity; rate of approximation; K-functional
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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MDPI and ACS Style

Ansari, K.J.; Ahmad, I.; Mursaleen, M.; Hussain, I. On Some Statistical Approximation by (p,q)-Bleimann, Butzer and Hahn Operators. Symmetry 2018, 10, 731.

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