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

摘要

In this paper, we prove a fixed point result for two maps in a generalized metric space (X, G). Also, we prove the 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 Φ-maps in G-metric spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 181650, 9 pages].