Around metric coincidence point theory

Let (X, d) be a complete metric space, (Y, rho) be a metric space and f, g : X-+ Y be two mappings. The problem is to give metric conditions which imply that, C(f, g) := {x E X | f (x) = g(x)} =6 0. In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, Teoria punctului fix in analiza funct,ionala, Babe,s-Bolyai Univ., Cluj-Napoca, 1973), A. Buica (A. Buica, Principii de coincident,a ,si aplicat,ii, Presa Univ. Clujeana, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, Covering mappings in metric spaces and fixed points, Dokl. Math., 76(2007), no.2, 665-668) appear as corollaries. In the case of multivalued mappings our result generalizes some results given by A.V. Arutyunov and by A. Petru,sel (A. Petru,sel, A generalization of Peetre-Rus theorem, Studia Univ. Babe,s-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied.