A Common Fixed Point for a Family of Compatible Maps Involving a Quasi-contraction on Cone Metric Spaces

Hassen Aydi

Abstract

In this paper, we establish a common fixed point result for a family of compatible maps satisfying a quasi-contraction on a complete cone metric space without assumption of normality condition of the cone. The result is an extension of a recent paper of Jankovic et al. [S. Jankovic, Z. Golubovic, S. Radenovic, Compatible and weakly compatible mappings in cone metric spaces, Math. Comput. Modelling 52 (2010) 1728--1738].