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

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  • Awad A. Bakery
  • Mustafa M. Mohammed

Abstract

An ideal I is a hereditary and additive family of subsets of positive integers 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 IL‐limit points and IL‐cluster points. Furthermore, Cauchy and IL‐Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:101782
DOI: 10.1155/2014/101782
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