In this paper we will characterize the completeness and barrelledness of a normed space through the strong p-Cesáro summability of series. A new characterization of weakly unconditionally Cauchy series and unconditionally convergent series through the strong p-Cesàro summability is obtained.
In this manuscript we characterize the completeness of a normed space through the strong lacunary ( N θ ) and lacunary statistical convergence ( S θ ) of series. A new characterization of weakly unconditionally Cauchy series through N θ and S θ is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesàro convergence summability space.
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