On relative uniform convergence of triple sequence of functions
Abstract
This paper discusses relative uniform convergence of triple sequence of functions that are defined on a compact domain. Another central idea that is discussed is the regular relative uniform convergence and the Cauchy relative uniform convergence of triple sequence of functions. The idea that a continuous triple sequence defined on a compact domain is relative uniform convergent if and only if it is relative uniform Cauchy has been discussed and established. Subsequently, a glimpse into Cesaro summability of triple sequences and a theorem regarding triple Cesaro summability of bounded relative uniform triple sequence of functions have been introduced.
Downloads
References
Bakery A. A, Mohamed O. M, Devi K. R, and Tripathy B. C. Cesaŕo summable relative uniform difference sequence of positive linear functions. Journal of Function Spaces, 2022, 3809939.
Chittenden E. W. Relatively uniform convergence of sequence of functions. Trans Amer Math Soc, 15 : 197–201, 1914.
Chittenden E. W. On the limit functions of sequence of continuous functions converging relatively uniformly. Trans Amer Math Soc, 20 : 179–184, 1919.
Chittenden E. W. Relative uniform convergence and classification of functions. Trans Amer Math Soc, 23 : 1–15, 1922.
Datta A. J, Esi A, and Tripathy B. C. Statistically convergent triple sequence spaces defined by orlicz function. J. Math. Anal, 4(2) : 16–22, 2013.
Debnath S, Sarma B, and Das B. Some generalized triple sequence spaces of real numbers. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 6(1) : 71–79, 2015.
Devi K. R and Tripathy B. C. Relative uniform convergence of difference double sequence of positive linear functions. Ricerche di Matematica, 72(2) : 961-972, 2023
Devi K. R and Tripathy B. C. On relative uniform convergence of double sequences of functions. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 92(3) : 367–372, 2022.
Devi K. R and Tripathy B. C. Relative uniform convergence of difference sequence of positive linear functions. Transactions of a Razmadze Mathematical Institute, 176(1) : 37–43, 2022.
Devi K. R and Tripathy B. C. Statistical relative uniform convergence of double sequence of positive linear functions. Palestine Journal of Mathematics, 11(3) : 558-570, 2022.
Hardy G. H. On the convergence of certain multiple series. Proc Camb Phil Soc, 19 : 86–95, 1917.
Moore E. H. Introduction to a form of general analysis, volume 2. Yale University Press, 1910.
Paikray S. K, Jena B. B, and Misra U. K. Statistical deferred cesàro summability mean based on (p, q)-integers with application to approximation theorems. In Advances in summability and approximation theory, pages 203–222. Springer, 2018.
Pringsheim A. Zur t’theorie der zweifach unendlichen zahlenfolgen. Math.Ann, 53 : 289–321, 1900.
Sahiner M, Gürdal A and Kadriye Düden F. Triple sequences and their statistical convergence. Math.Ann, 53 : 289–321, 1900.
Srivastava H. M, Jena B. B, Paikray S. K, and Misra U. K. Statistically and relatively modular deferred-weighted summability and korovkin-type approximation theorems. Symmetry, 11(4) : 448, 2019.
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
