Approximation by Generalized Lupa? Operators Based on q -Integers

Mohd Qasim, M. Mursaleen, Asif Khan and Zaheer Abbas
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Mohd Qasim: Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Rajouri 185234, Jammu and Kashmir, India
M. Mursaleen: Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40402, Taiwan
Asif Khan: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Zaheer Abbas: Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Rajouri 185234, Jammu and Kashmir, India

Mathematics, 2020, vol. 8, issue 1, 1-15

Abstract: The purpose of this paper is to introduce q -analogues of generalized Lupa? 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 Lupa? operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.

Keywords: generalized Lupa? operators; q analogue; Korovkin’s type theorem; convergence theorems; Voronovskaya type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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