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On Lacunary Mean Ideal Convergence in Generalized Random -Normed Spaces

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  • Awad A. Bakery
  • Mustafa M. Mohammed

Abstract

An ideal is a hereditary and additive family of subsets of positive integers . In this paper, we will introduce the concept of generalized random -normed space as an extension of random -normed space. Also, we study the concept of lacunary mean ( )-ideal convergence and -ideal Cauchy for sequences of complex numbers in the generalized random -norm. We introduce -limit points and -cluster points. Furthermore, Cauchy and -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 -Normed Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, April.
    • Handle: RePEc:hin:jnlaaa:101782
    DOI: 10.1155/2014/101782
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    Cited by:

    1. Donal O’Regan & Reza Saadati & Chenkuan Li & Fahd Jarad, 2022. "The Hausdorff–Pompeiu Distance in Gn -Menger Fractal Spaces," Mathematics, MDPI, vol. 10(16), pages 1-11, August.

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