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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.

Suggested Citation

  • Awad A. Bakery & Mustafa M. Mohammed, 2014. "On Lacunary Mean Ideal Convergence in Generalized Random n‐Normed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:101782
    DOI: 10.1155/2014/101782
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    References listed on IDEAS

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    1. Awad A. Bakery & Elsayed Abdelbayen Elnour Mohamed & Mohamed Alamin Ahmed, 2013. "Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak‐Orlicz Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Awad A. Bakery & Elsayed Abdelbayen Elnour Mohamed & Mohamed Alamin Ahmed, 2013. "Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, June.
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    1. Awad A. Bakery, 2013. "Generalized Difference λ‐Sequence Spaces Defined by Ideal Convergence and the Musielak‐Orlicz Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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