Some Geometric Properties of Generalized Difference Cesaro Sequence Spaces

Abstract

In this paper, we definethe generalized Ces\`{a}ro difference sequence space $C_{\left(p\right) }(\Delta^{m})$ and consider it equipped with the Luxemburgnorm under which it is a Banach space and we show that in the space $C_{\left( p\right) }(\Delta^{m})$ every weakly convergent sequenceon the unit sphere converges is the norm$,$ where $p=(p_{n})$ is abounded sequence of positive real numbers with $p_{n}>1$ for all $n\in \mathbb{N}$.