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.
Highlights
Introduction and preliminariesThe notion of statistical convergence, which is an extension of the idea of common convergence, was first appeared, under the name of almost convergence, in the first edition of the celebrated monograph of Zygmund [32]
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 by supporting an illustrative example
The statistical convergence was studied in various setup such as topological Hausdorff groups [8], normed spaces [15], locally convex Hausdorff topological spaces [16], paranormed spaces [2], random 2-normed spaces [19] and many others
Summary
Introduction and preliminariesThe notion of statistical convergence, which is an extension of the idea of common convergence, was first appeared, under the name of almost convergence, in the first edition of the celebrated monograph of Zygmund [32]. We 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. Double sequence; statistical convergence; statistical Cauchy; strong p-Cesaro summability; paranormed space.
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