Some geometric properties of a new difference sequence space defined by de la Vallée-Poussin mean

In this paper, wedefine a new generalized difference sequence space CpΔλm and consider it equipped with the Luxemburg norm under which it is a Banach space and we show that the space CpΔλm possess Banach Saks property of type p, uniform opial property and property (H), where p=(pn) is a bounded sequence of positive real numbers with pn>1 for all n∈N. Also, we give some results about the fixed point theory for the spaces CpΔm and CpΔm1