Common fixed point result for two self-maps in $G$-metric spaces

Abstract

In this paper, we prove a fixed point result for two maps in a generalized metric space $(X,G)$. Also, we provethe uniqueness of such fixed point. This result generalizes some well known results in the literature due to M. Abbas and B.E. Rhoades [Common fixed point results for noncommuting mapping without continuity in generalized metric spaces, Appl. Math. Computation 215(2009), 262–269] and W. Shatanawi [Fixed point theory for contractive mappings satisfying $\Phi$-maps in $G$-metric spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 181650, 9 pages].