On I-convergence in random 2-normed spaces

Abstract

ABSTRACT. Recently the concepts of statistical convergence and ideal convergence have been studied in 2-normed and 2-Banach spaces by various authors. In this paper we define and study the notion of ideal convergence in random 2-normed space and construct some interesting examples.

Lacunary generalized difference statistical convergence in random 2-normed spaces

“…In fact, Mursaleen [22] studied the concept of statistical convergence of sequences in random 2-normed spaces, in [24], Mohiuddine and Aiyub introduced the concept of lacunary statistical convergence in random 2-normed space. Recently in [4], Esi and Ozdemir introduced and studied the concept of generalized ∆ m -statistical convergence of sequences in probabilistic normed spaces and in [5] Esi and Ozdemir introduced and studied the concept of lacunary statistical convergence in random n-normed space.…”

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AbstractRecently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary ∆ n -statistical convergence and lacunary ∆ n -statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems.

Subjclass [2000] :

Primary 40A05; Secondary 46A70, 40A99, 46A99.

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On the Ulam Stability of Cauchy Functional Equation in IFN-Spaces

“…Quite recently, Chang [5] has established the stability of higher ring derivation in intuitionistic fuzzy Banach algebras associated to the Jensen type functional equation. In the recent past, Alotaibi and Mohiuddine [2] established the Ulam stability of a cubic functional equation in random 2-normed spaces, while the notion of random 2-normed spaces was introduced by Goleţ [8] and further studied in [18,26,21]. Now, we recall some notations and basic definitions which will be used throughout the paper.…”

$\mathcal{I}$ and $\mathcal{I}^{\ast}$ convergence of multiple sequences of fuzzy numbers

“…The credit goes to Kumar et al [17] who first defined I-convergence for sequences of fuzzy numbers. For an extensive view of this subject, we refer [2,5,10,11,12,13,16,23].…”