Abstract :
Let (X, d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we
study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the
contractive condition (2.1) below, and a class of pairs of mappings fromK into X which satisfy the condition
(2.28) below. We present fixed point and common fixed point theorems which are generalizations of the
corresponding fixed point theorems of C´ iric´ [L.B. C´ iric´, Quasi-contraction non-self mappings on Banach
spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25–31; L.B. C´ iric´, J.S. Ume, M.S. Khan, H.K.T. Pathak, On
some non-self mappings, Math. Nachr. 251 (2003) 28–33], Rhoades [B.E. Rhoades, A fixed point theorem
for some non-self mappings, Math. Japon. 23 (1978) 457–459] and many other authors. Some examples are
presented to show that our results are genuine generalizations of known results from this area.
2005 Elsevier Inc. All rights reserved.
