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On generalized difference ideal convergence in random 2-normed spaces

Hazarika Bipan (Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh- , Arunachal Pradesh, India)

An ideal I is a family of subsets of positive integers 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 (xk ) of real numbers is said to be I-convergent to a real number ℓ, if for each ε > 0 the set {k ∈ N : |xk − ℓ| ≥ ε} belongs to I. In [28], Mursaleen and Alotaibi introduced the concept of I-convergence of sequences in random 2-normed spaces. In this paper, we define and study the notion of ∆n -ideal convergence and ∆n -ideal Cauchy sequences in random 2-normed spaces, and prove some interesting theorems.

Keywords: I-convergence, difference sequence, t-norm, 2-norm, random 2-normed space