Thai Journal of Mathematics Volume 3 (2005) Number 2 : 193–199 A Common Fixed Point Theorem for a Pair of Nonself Multi-valued Mappings M. Imdad and Ladlay Khan Abstract : A common fixed point theorem for a pair of nonself multi-valued mappings in complete metrically convex metric spaces is proved which generalizes some earlier known results due to Khan et al. [9], Bianchini [2], Chatterjea [3], Khan et al. [10] and others. An illustrative example is also discussed. Keywords : Metrically convex metric spaces, multi-valued mappings, fixed point. 2000 Mathematics Subject Classification : 54H25, 47H10. 1 Introduction The study of fixed point theorems for nonself multi-valued contractions on metrically convex metric spaces was initiated by Assad and Kirk [1]. In recent years, several fixed point theorems for such maps were proved which include rele- vant results due to Rhoades [12, 13], Hadˇ zi` c and Gajic [4], Is´ eki [5], Itoh [6], Khan [8] and others. The purpose of this paper is to extend a fixed point theorem due to Khan et al. [9] proved for nonself single valued mappings to a pair of multi-valued nonself mappings. For the sake of completeness, we state Theorem 1 due to Khan et al. [9]. Theorem 1.1 Let (X, d) be a complete metrically convex metric space and K a nonempty closed subset of X. Let T : K → X be a mapping satisfying the inequality d(Tx,Ty) ≤ a max{d(x, T x),d(y,Ty)} + b {d(x, T y)+ d(y,Tx)} (1) for every x, y ∈ K, where a and b are non-negative reals such that max  a + b 1 - b , b 1 - a - b  = h> 0, max  1+ a + b 1 - b h, 1+ b 1 - a - b h  = h  , and max{h, h  } = h  < 1. Further, if for every x ∈ δK, Tx ∈ K, then T has a unique fixed point in K.