On Generalized Difference Ideal Convergence in Random 2-Normed Spaces

Bipan Hazarika

An ideal $I$ is a family of subsets of positive integers \textbf{N} which is closed under taking finite unions and subsets of its elements. In [17], Kostyrko et. al introduced the concept of ideal convergence as a sequence ($x_k$) of real numbers is said to be $I$-convergent to a real number $l$, if for each $\epsilon >0$ the set $\{k \in \textbf{N}:|x_k-l|\geq \epsilon\}$ belongs to $I$. In [28], Mursaleen and Alotaibi introduced the concept of $I$-convergence of sequences in random 2-normed spaces. We define and study the notion of $\Delta^n$-ideal convergence and $\Delta^n$-ideal Cauchy sequences in random 2-normed spaces, and prove some interesting theorems.