International Journal of Nonlinear Analysis and Applications

New results on $ f $-statistical convergence of order $ \tilde{\alpha} $ through triple sequences spaces

Articles in Press

Document Type : Research Paper

Authors

1 Escuela Ciencias de la Educacion, Universidad Nacional Abierta y a Distancia, Barranquilla, Colombia

2 Department of Mathematics, Faculty of Sciences, Bartin University, 74100 Bartin, Turkey

10.22075/ijnaa.2022.25758.3119

Abstract

In this paper, we define new notions of $ f $-statistical convergence for triple sequences of order $ \tilde{\alpha}$ and strong $ f $-Cesaro summability for triple sequences of order $ \tilde{\alpha} $. Moreover we show the relationship between the spaces $ w_{\tilde{\alpha},0}^{3}(f) $, $ w_{\tilde{\alpha}}^{3}(f) $ and $ w_{\tilde{\alpha},\infty}^{3}(f) $. Additionally, we show some properties of the strong $ f $-Cesaro summability of order $ \tilde{\beta} $. The main purpose of this paper is to examine the concept of $f$-triple statistical convergence of order $\alpha $; where $f$-is an unbounded function and give relations between $f$-triple statistical convergence of order $\alpha $ and strong $f$-Ces\`aro summability for a triple sequence of order $\alpha $.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 18 March 2025
  • Receive Date: 31 December 2021
  • Revise Date: 27 May 2022
  • Accept Date: 11 June 2022