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On \(k\)-nearly uniform convex property in generalized Cesàro sequence spaces. (English) Zbl 1039.46016
Summary: We define a generalized Cesàro sequence space \(\text{ces}(p)\), where \(p=(p_{k})\) is a bounded sequence of positive real numbers, and consider it equipped with the Luxemburg norm. The main purpose of this paper is to show that \(\text{ces}(p)\) is \(k\)-nearly uniform convex (\(k\)-NUC) for \(k\geq 2\) when \(\text{lim}_ {n \rightarrow \infty} \inf p_{n}>1\). Moreover, we also obtain that the Cesàro sequence space \(\text{ces}_{p}\), where \(1<p< \infty,\) is \(k\)-NUC, \(kR\), NUC, and has the drop property.

MSC:
46B45 Banach sequence spaces
46B20 Geometry and structure of normed linear spaces
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