Regularly ideal convergence and regularly ideal cauchy double sequences in 2-normed spaces

Abstract

In this paper, we introduce the notions of (I2,I), (I*2,I*)-convergence and (I2,I), (I*2,I*)- Cauchy double sequence in regular sense in 2-normed spaces. Also, we study some properties of these concepts.

Influence of ideals in compactifications

“…After a long, in the year 2001, Kostyrko et al [1] introduced the concept of I-convergence using the notion of ideals. During last two decades research on the theory of I-convergence have been reached in the peak [3], [4], [5], [6], [10], [12] etc..…”

ON $\mathcal{I}_2$-CONVERGENCE AND $\mathcal{I}_2$-CAUCHY DOUBLE SEQUENCES OF FUNCTIONS IN 2-NORMED SPACES

“…Recently, Arslan and Dündar [1,2] inroduced I-convergence and I-Cauchy sequences of functions in 2-normed spaces. Futhermore, there has been a lot of development in this area (see [3,4,6,26,27,29,[31][32][33][37][38][39]).…”

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

“…Recently, Arslan and Dündar [1,2] inroduced I -convergence and I -Cauchy sequences of functions in 2-normed spaces. Futhermore, a lot of development have been made in this area (see [3,5,13,26,30,33]).…”