On k-nearly uniform convex property in generalized Cesàro sequence spaces

Abstract

We define a generalized Cesàro sequence space ces(p), where p=(pk) 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 ces(p) is k-nearly uniform convex (k-NUC) for k≥2 when limn→∞infpn>1. Moreover, we also obtain that the Cesàro sequence space cesp(where 1<p<∞) is k-NUC, kR, NUC, and has a drop property.