Ideal convergence of double sequences in random 2-normed spaces

被引：27

作者：

Mohiuddine, Syed Abdul ^{[1
]}

Alotaibi, Abdullah ^{[1
]}

Alsulami, Saud M. ^{[1
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2012年

关键词：

double sequences; t-norm; random 2-normed spaces; ideal convergence; LACUNARY STATISTICAL CONVERGENCE; I-CONVERGENCE;

D O I：

10.1186/1687-1847-2012-149

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Quite recently, Alotaibi and Mohiuddine (Adv. Differ. Equ. 2012: 39, 2012) studied the idea of a random 2-normed space to determine some stability results concerning the cubic functional equation. In this paper, we define and study the concepts of I-convergence and I*-convergence for double sequences in random 2-normed spaces and establish the relationship between these types of convergence, i.e., we show that I*-convergence implies I-convergence in random 2-normed spaces. Furthermore, we have also demonstrated through an example that, in general, I-convergence does not imply I*-convergence in random 2-normed spaces.

引用

页数：8

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