Some Geometric Properties of Generalized Difference Ces`aro Sequence Spaces

Abstract

: In this paper, we define the generalized Ces`aro difference sequence space C(p)(∆m) and consider it equipped with the Luxemburg norm under which it is a Banach space and we show that in the space C(p)(∆m) every weakly convergent sequence on the unit sphere converges is the norm, where p = (pn) is a bounded sequence of positive real numbers with pn > 1 for all n ∈ N