Abstract and Applied Analysis

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

Awad A. Bakery and Mustafa M. Mohammed

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Abstract

An ideal I is a hereditary and additive family of subsets of positive integers . 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

Permanent link to this document
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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