Abstract :
Jungck’s [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9
(1986) 771–779] notion of compatible mappings is further extended and used to prove some common
fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces.We
improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self
set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9–12] and Ahmed and Rhoades [A. Ahmed,
B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl.
Math. 32 (2001) 1247–1254] and obtain generalization of some known results. In particular, a theorem
by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J.Math.
Math. Sci. 20 (1997) 9–12] is generalized and improved.
2005 Elsevier Inc. All rights reserved.
