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Matematicheskie Zametki, 2019, Volume 105, Issue 6, paper published in the English version journal (Mi mzm12482)  
Papers published in the English version of the journal

A Short Note on a $q$-Analog of Modified Stancu–Beta Operators

P. Sharma, G. S. Rathore

Department of Mathematics and Statistics, University College of Science, Mohanlal Sukhadia University, Udaipur-313001 (Rajasthan), India
Abstract: This paper deals with the modified $q$-Stancu–Beta operators and investigates statistical approximation theorems for these operators with the help of a Korovkin-type approximation theorem. The rates of statistical convergence are determined by means of the modulus of continuity and a Lipschitz-type maximal function. The results show that the rates of convergence of the operators under consideration are at least as fast as those of the classical Stancu–Beta operators.
Keywords: $q$-integers, statistical convergence, $q$-Stancu–Beta operators, rate of statistical convergence, modulus of continuity, positive linear operators, Korovkin-type approximation theorem.
Received: 30.09.2018
Revised: 10.02.2019
English version:
Mathematical Notes, 2019, Volume 105, Issue 6, Pages 881–887
DOI: https://doi.org/10.1134/S0001434619050250
Bibliographic databases:
Document Type: Article
Language: English
Citation: P. Sharma, G. S. Rathore, “A Short Note on a $q$-Analog of Modified Stancu–Beta Operators”, Math. Notes, 105:6 (2019), 881–887
Citation in format AMSBIB
\Bibitem{ShaRat19}
\by P.~Sharma, G.~S.~Rathore
\paper A Short Note on a $q$-Analog of Modified Stancu--Beta Operators
\jour Math. Notes
\yr 2019
\vol 105
\issue 6
\pages 881--887
\mathnet{http://mi.mathnet.ru/mzm12482}
\crossref{https://doi.org/10.1134/S0001434619050250}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3976544}
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\elib{https://elibrary.ru/item.asp?id=42052642}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068112618}
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