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Open AccessArticle

Approximation by Generalized Lupaş Operators Based on q-Integers

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Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Rajouri 185234, Jammu and Kashmir, India
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Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40402, Taiwan
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Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
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Department of Computer Science and Information Engineering, Asia University, Taichung 41354, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 68; https://doi.org/10.3390/math8010068
Received: 6 December 2019 / Revised: 25 December 2019 / Accepted: 27 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation. View Full-Text
Keywords: generalized Lupaş operators; q analogue; Korovkin’s type theorem; convergence theorems; Voronovskaya type theorem generalized Lupaş operators; q analogue; Korovkin’s type theorem; convergence theorems; Voronovskaya type theorem
MDPI and ACS Style

Qasim, M.; Mursaleen, M.; Khan, A.; Abbas, Z. Approximation by Generalized Lupaş Operators Based on q-Integers. Mathematics 2020, 8, 68.

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