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Asymptotic equivalence and summability

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  • Mousa S. Marouf

Abstract

This paper is a study of the relatioship. between the asymptotic equivalence of two sequences ( lim n x n / y n = 1 ) and three variatious of this equivalence for a sequence-to-sequence transformation A , the three variations are give by the ratios R m A x / R m A y . S m A x / S m A y , And μ m A x / μ m A y , where R m A z : = ∑ n ≥ m | ( A z ) n | , S m A z : = ∑ n ≤ m | ( A z ) n | , and μ m A z : = sup n ≥ m | ( A z ) n | .

Suggested Citation

  • Mousa S. Marouf, 1993. "Asymptotic equivalence and summability," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:970869
    DOI: 10.1155/S0161171293000948
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    Cited by:

    1. Tunay Bilgin, 2014. "-Asymptotically Lacunary Equivalent Sequences," International Journal of Analysis, Hindawi, vol. 2014, pages 1-8, December.
    2. Uğur Ulusu & Fatih Nuray, 2013. "On Asymptotically Lacunary Statistical Equivalent Set Sequences," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, March.

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