Statistically Riemann integrable and Summable Sequence of Functions via Deferred Cesàro Mean

In this article, we introduced the concepts of statistical Riemann integrability, deferred Cesàro statistical Riemann integrability and statistical deferred Cesàro Riemann summability for sequence of real-valued functions. We first established some fundamental theorems connecting these concepts with...

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Bibliographic Details
Published in:Bulletin of the Iranian Mathematical Society 2022-08, Vol.48 (4), p.1293-1309
Main Authors: Jena, Bidu Bhusan, Paikray, Susanta Kumar, Dutta, Hemen
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Paper
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Summary:In this article, we introduced the concepts of statistical Riemann integrability, deferred Cesàro statistical Riemann integrability and statistical deferred Cesàro Riemann summability for sequence of real-valued functions. We first established some fundamental theorems connecting these concepts with examples. Then, we developed a criteria for statistical Cauchy–Riemann integrability and a theorem in this connection has been given. Application of the newly introduced Riemann integrability of sequence of functions has been shown with the help of certain new Korovkin-type approximation results, and demonstrated some more interesting results with relevant examples for positive linear operators. We also highlighted some important aspects of our findings in the conclusion section.
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-021-00578-8