Sanhan, Winate; Suantai, Suthep On \(k\)-nearly uniform convex property in generalized Cesàro sequence spaces. (English) Zbl 1039.46016 Int. J. Math. Math. Sci. 2003, No. 57, 3599-3607 (2003). 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. Cited in 16 Documents MSC: 46B45 Banach sequence spaces 46B20 Geometry and structure of normed linear spaces Keywords:Cesàro sequence space; \(k\)-nearly uniform convex; drop property PDFBibTeX XMLCite \textit{W. Sanhan} and \textit{S. Suantai}, Int. J. Math. Math. Sci. 2003, No. 57, 3599--3607 (2003; Zbl 1039.46016) Full Text: DOI EuDML