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Journal of Classical Analysis
Article . 2023 . Peer-reviewed
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zbMATH Open
Article . 2023
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Modified Jain-Pethe-Baskakov-Durrmeyer operators and their quantitative estimates

Authors: Sharma, Honey; Maurya, Ramapati;

Modified Jain-Pethe-Baskakov-Durrmeyer operators and their quantitative estimates

Abstract

Summary: In this paper, we present a modification of Jain-Pethe-Baskakov-Durrmeyer operators and estimate their moments. Then, we establish the uniform convergence of the proposed family of operators. Further, we use modulus of continuity and \(K\)-functional to establish local approximation behavior of these operators. Also, we compute the rate of convergence of the operators through Lipschitz class functions. In the last section, we present some quantitative results for difference of the proposed operators with Jain-Pethe operators and Durrmeyer type variant of Jain-Pethe-Baskakov operators.

Keywords

modulus of continuity, Approximation by operators (in particular, by integral operators), Baskakov operators, Peetre's \(K\)-functional, Rate of convergence, degree of approximation, \(\beta\) function, Jain-Pethe operators

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
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