Around metric coincidence point theory

Let $(X,d)$ be a complete metric space, $(Y,\rho)$ space and $f,g:X\to Y$ two mappings. The problem is to give conditions which imply that, $C(f,g):=\{x\in X\ |\ f(x)=g(x)\}\not=\emptyset$. In this paper we an abstract coincidence point result with respect some results such as of Peetre-Rus (I.A. Rus, \emph{Teoria punctului fix \^in analiza func\c tional\u a}, Babe\c s-Bolyai Univ., Cluj-Napoca, 1973), A. Buic\u (A. a, \emph{Principii de coinciden\c t\u \c si aplica\c tii}, Presa Univ. Clujean\u 2001) A.V. Arutyunov (A.V. Arutyunov, \emph{Co\-vering mappings in spaces fixed points}, Dokl. Math., 76(2007), no.2, 665-668) appear corollaries. the case multivalued our generalizes given by Petru\c sel sel, \emph{A generalization theorem}, Studia 35(1990), 81-85). impact on theory also studied.