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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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