## Abstract and Applied Analysis

### On Lacunary Mean Ideal Convergence in Generalized Random $n$-Normed Spaces

#### Abstract

An ideal $I$ is a hereditary and additive family of subsets of positive integers $\Bbb N$. In this paper, we will introduce the concept of generalized random $n$-normed space as an extension of random $n$-normed space. Also, we study the concept of lacunary mean ($L$)-ideal convergence and $L$-ideal Cauchy for sequences of complex numbers in the generalized random $n$-norm. We introduce ${I}_{L}$-limit points and ${I}_{L}$-cluster points. Furthermore, Cauchy and ${I}_{L}$-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 101782, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276934

Digital Object Identifier
doi:10.1155/2014/101782

Mathematical Reviews number (MathSciNet)
MR3200765

Zentralblatt MATH identifier
07021733

#### Citation

Bakery, Awad A.; Mohammed, Mustafa M. On Lacunary Mean Ideal Convergence in Generalized Random $n$ -Normed Spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 101782, 11 pages. doi:10.1155/2014/101782. https://projecteuclid.org/euclid.aaa/1412276934

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