Two Fixed Point Theorems in Topological vector space Valued Cone Metric Spaces with Complete Topological Algebra Cones

Abstract

In this paper we prove two fixed point theorems in topological vector space valued cone metric spaces (briefly TVS-CMS).To that end we introduce the concept of complete topological algebra cone (briefly CTA cone).Our theorems are generalizations of corresponding theorems in [8] and [13].The paper also gives answers to the open problems posed in [15].Finally we give an application of our first theorem.