Well-posedness and Common Fixed Points for Two Pairs of Maps Using Weak Contractivity

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contraction, Appl. Math. Lett. 22(2009), 75-78] and [D. Dorić, Common fixed point for generalized (ψ, φ)-weak contractions, Appl. Math. Lett., 22(2009), 1896-1900] to prove a common fixed point theorem for four mappings satisfying generalized weak contractive condition (see Filomat 24:2 (2010), 1-10). In this paper we generalize this theorem by using the concept of common property (E.A). Our result generalizes and unifies several existing results involving generalized weak contractive conditions. We study also well-posedness of a related fixed point problem.