Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2009, Article ID 131068, 9 pages doi:10.1155/2009/131068 Research Article Common Fixed Point Theorem of Two Mappings Satisfying a Generalized Weak Contractive Condition M. Abbas and M. Ali Khan Department of Mathematics, Lahore University of Management Sciences, Lahore 54792, Pakistan Correspondence should be addressed to M. Abbas, mujahid@lums.edu.pk Received 6 August 2009; Accepted 11 November 2009 Recommended by Evgeny Korotyaev Existence of common fixed point for two mappings which satisfy a generalized weak contractive condition is established. As a consequence, a common fixed point result for mappings satisfying a contractive condition of integral type is obtained. Our results generalize, extend, and unify several well-known comparable results in literature. Copyright q 2009 M. Abbas and M. A. Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction and Preliminaries Let X be a metric space and T : C → C a mapping. Recall that T is contraction if dTx,Ty ≤ kdx, y for all x, y ∈ X, where 0 ≤ k< 1. A point x ∈ C is a fixed point of T provided Tx  x. If a map T satisfies FT  FT n  for each n ∈ N, where FT  denotes the set of all fixed points of T, then it is said to have property P. Banach contraction principle which gives an answer on existence and uniqueness of a solution of an operator equation Tx  x is the most widely used fixed point theorem in all of analysis. Branciari 1 obtained a fixed point theorem for a mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Akgun and Rhoades 2 have shown that a map satisfying a Meir- Keeler type contractive condition of integral type has a property P. Rhoades and Abbas 3 extended 4, Theorem 1 for mappings satisfying contractive condition of integral type. They also studied several results for maps which have property P, defined on a metric space satisfying generalized contractive conditions of integral type. Rhoades 5 proved two fixed point theorems involving more general contractive condition of integral type see, also 6, 7. If maps S and T satisfy FS ∩ FT  FS n  ∩ FT n  for each n ∈ N, then they are said to have property Q. Jeong and Rhoades 8 studied the property Q for pairs of maps satisfying a number of contractive conditions.