• A COMMON FIXED POINT THEOREM FOR TWO SELF MAPS ON A CONE METRIC SPACE WITH CONVEX PROPERTY

K. P. R. Sastry, G. Appala Naidu, P. Chandana Lakshmi*, Tadesse Bekeshie

Abstract


In this paper we introduce the notion of convex property in cone metric spaces. We show that a cone convex metric space has convex property. We also show that there are cone metric spaces with convex property, which are not cone convex metric spaces. We prove a common fixed point theorem for two self maps on a cone metric space with convex property and obtain the corresponding result on cone convex metric spaces as a corollary. An open problem is also given at the end of the paper.

Keywords


Convex property, convex structure, Cone convex metric space, common fixed point theorem.

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