$\mathcal{I}_2$-Uniform Convergence of Double Sequences of Functions In $2$-Normed Spaces-Reference-Cited by-同舟云学术

$\mathcal{I}_2$-Uniform Convergence of Double Sequences of Functions In $2$-Normed Spaces

Published:2022-10-01 Issue: Volume: Page:
ISSN:2651-4001
Container-title:Communications in Advanced Mathematical Sciences
language:en
Short-container-title:

Author:

YEGÜL GÜZEY Sevim,DÜNDAR Erdinç¹,ARSLAN Mukaddes

Affiliation:

1. AFYON KOCATEPE ÜNİVERSİTESİ

Abstract

In this work, we discuss various kinds of $\mathcal{I}_2$-uniform convergence and equi-continuous for double sequences of functions and introduce the concepts of $\mathcal{I}_2$-uniform convergence, $\mathcal{I}_2^*$-uniform convergence, $\mathcal{I}_2$-uniformly Cauchy sequences and $\mathcal{I}_2^*$-uniformly Cauchy sequences for double sequences of functions in $2$-normed spaces. Then, we show the relationships between them.

Publisher

Communications in Advanced Mathematical Sciences

Subject

General Medicine

Reference40 articles.

1. [1] M. Arslan, E. Dündar, I-Convergence and I-Cauchy Sequence of Functions In 2-Normed Spaces, Konuralp Journal of Mathematics, 6(1) (2018), 57–62.

2. [2] M. Arslan, E. Dündar, On I-Convergence of sequences of functions in 2-normed spaces, Southeast Asian Bulletin of Mathematics, 42 (2018), 491–502.

3. [3] M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bulletin of Mathematical Analysis and Applications, 10(3) (2018), 1–9.

4. [4] M. Arslan, E. Dündar, On Rough Convergence in 2-Normed Spaces and Some Properties Filomat 33(16) (2019), 5077–5086.

5. [5] V. Baláz, J. ˘Cerve˘nanský, P. Kostyrko, T. ˘Salát, I-convergence and I-continuity of real functions, Acta Mathematica, Faculty of Natural Sciences, Constantine the Philosopher University, Nitra, 5 (2004), 43–50.