On variations of quasi-cauchy sequences in cone metric spaces

Abstract

sequence (xn) of points in a topological vector space valued cone metric space (X,?) is called p-quasi-Cauchy if for each c ??K there exists an n0 ? N such that ?(xn+p,xn)- c ??K for n ? n0, where K is a proper, closed and convex pointed cone in a topological vector space Y with ?K?0. We investigate p-ward continuity in topological vector space valued cone metric spaces. It turns out that p-ward continuity coincides with uniform continuity not only on a totally bounded subset but also on a connected subset of X.