Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

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Abdullah Alotaibi, Alaa Mohammed Aljahili, S.A. Mohiuddine, Generalized Statistical Convergence of Double Sequences in Paranormed Spaces, Int. J. Anal. Appl., 17 (5) (2019), 711-721.

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Abdullah Alotaibi, Alaa Mohammed Aljahili, S.A. Mohiuddine

Abstract

We introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy and strongly (λ, µ)p-summable double sequences in a paranormed space and obtain their relationship with (λ, µ)- statistical convergence.

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