Point of Coincidence and Common Fixed Points of a Pair of Generalized Weakly Contractive Maps

We prove the existence of a point of coincidence for a pair of selfmaps $(f,~T)$ of a metric space $(X,d)$ in which $T$ is a generalized weakly contractive map with respect to $f$, through the convergence of the Picard iteration (Theorem 3.2). Also, we deduce the existence of common fixed points for occasionally weakly compatible maps (Theorem 3.3). Further, we prove the existence of common fixed points for a pair of occasionally weakly compatible selfmaps satisfying generalized weakly contractive condition and property (E.A). Our results generalize the corresponding results of Babu and Alemayehu [6], Beg and Abbas [7] and Rhoades [14] when the space under consideration is bounded.