| Autor: |
T. Pradhan, S. K. Paikray, B. B. Jena, H. Dutta |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Journal of Inequalities and Applications, Vol 2018, Iss 1, Pp 1-21 (2018) |
| Druh dokumentu: |
article |
| ISSN: |
1029-242X |
| DOI: |
10.1186/s13660-018-1650-x |
| Popis: |
Abstract The notion of statistical weighted B $\mathcal{B}$-summability was introduced very recently (Kadak et al. in Appl. Math. Comput. 302:80–96, 2017). In the paper, we study the concept of statistical deferred weighted B $\mathcal{B}$-summability and deferred weighted B $\mathcal{B}$-statistical convergence and then establish an inclusion relation between them. In particular, based on our proposed methods, we establish a new Korovkin-type approximation theorem for the functions of two variables defined on a Banach space CB(D) $C_{B}(\mathcal{D})$ and then present an illustrative example to show that our result is a non-trivial extension of some traditional and statistical versions of Korovkin-type approximation theorems which were demonstrated in the earlier works. Furthermore, we establish another result for the rate of deferred weighted B $\mathcal{B}$-statistical convergence for the same set of functions via modulus of continuity. Finally, we consider a number of interesting special cases and illustrative examples in support of our findings of this paper. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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