Lacunary ideal convergence of multiple sequences

Abstract

An ideal I is a family of subsets of N Â N which is closed under taking finite unions and subsets of its elements. In this article, the concept of lacunary ideal convergence of double sequences has been introduced. Also the relation between lacunary ideal convergent and lacunary Cauchy double sequences has been established. Furthermore, the notions of lacunary ideal limit point and lacunary ideal cluster points have been introduced and find the relation between these two notions. Finally, we have studied the properties such as solidity, monotonic. 2010 AMS CLASSIFICATION NO: 40A05; 40G15; 46D05; 46A45 ª 2015 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.

Fibonacci Lacunary Ideal Convergence of Double Sequences in Intuitionistic Fuzzy Normed Linear Spaces

“…Lacunary ideal convergence of real sequences was introduced by Tripathy et al [28]. This kind of convergence extended from single to double sequences with the study of Hazarika [8]. For different studies on these topic we refer to [3,4,21].…”

On Generalized Statistical Convergence of Double Sequences via Ideals in Intuitionistic Fuzzy Normed Spaces

“…Belen et al [5] generalized the notions of statistical convergence, (λ, µ)-statistical convergence, (V, λ, µ) summability and (C, 1, 1) summability for a double sequence via ideals. The other studies of this concept were examined by [21,33,41,42,44,45,47].…”

Rough I 2 ${I}_{2}$ -lacunary statistical convergence of double sequences

“…Kumar et al [33] introduced -lacunary statistical convergence of double sequences. Further investigation and applications on this notion can be found in [34]. …”