Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the conver...

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Bibliographic Details
Published in:	Journal of applied mathematics & computing Vol. 65; no. 1-2; pp. 429 - 450
Main Authors:	Braha, Naim L., Srivastava, H. M., Et, Mikail
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-02-2021 Springer Nature B.V
Subjects:	Applied mathematics Computational Mathematics and Numerical Analysis Convergence Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Original Research Theorems Theory of Computation Sequence spaces Korovkin type theorem 41A36 Voronovskaya type theorem 46A45 46A35 Rate of convergence 40G15 Weighted statistical convergence
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Summary:	In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.
ISSN:	1598-5865 1865-2085
DOI:	10.1007/s12190-020-01398-5