Nonlinear Analysis 67 (2007) 2717–2726 www.elsevier.com/locate/na Some common fixed point theorems for a family of mappings in metrically convex spaces M. Imdad, Ladlay Khan ∗ Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India Received 10 April 2006; accepted 19 September 2006 Abstract In the present paper some common fixed point theorems for a sequence and a pair of nonself-mappings in complete metrically convex metric spaces are proved which generalize such results due to Khan et al. [M.S. Khan, H.K. Pathak, M.D. Khan, Some fixed point theorems in metrically convex spaces, Georgian Math. J. 7 (3) (2000) 523–530], Assad [N.A. Assad, On a fixed point theorem of Kannan in Banach spaces, Tamkang J. Math. 7 (1976) 91–94], Chatterjea [S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972) 727–730] and several others. Some related results are also discussed. c  2006 Elsevier Ltd. All rights reserved. Keywords: Metrically convex metric space; Weak commutativity; Compatible mappings; Pointwise R-weak commutativity; Complete metric space 1. Introduction The existing literature of fixed point theory contains many results enunciating fixed point theorems for self- mappings in metric and Banach spaces. But fixed point theorems for nonself-mappings are not frequently discussed and so form a natural subject for further investigation. The study of fixed point theorems for nonself-mappings in metrically convex metric spaces was initiated by Assad and Kirk [1]. Indeed while doing so, Assad and Kirk [1] noticed that with the realization of some kind of metric convexity in the metric spaces, the domain and range of the mappings under investigation can be of a more varied type. In the same setting Rhoades [12] and Assad [2] continued to prove results enunciating sufficient conditions for the existence of fixed points. Motivated by Hadˇ zi´ c[4] and Sessa et al. [14], we prove a common fixed point theorem for a family of nonself- mappings comprising two single-valued maps and a sequence of maps defined on a nonempty closed subset K of the metric space ( X , d ). The contraction condition employed is essentially patterned after Khan et al. [10]. Besides our main result (i.e. Theorem 3.1), we have also discussed some related results. Here for the sake of completeness, we state (cf. [10, Theorem 1]) the following. 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 d (Tx , Ty ) ≤ a max{d (x , Tx ), d ( y , Ty )}+ b{d (x , Ty ) + d ( y , Tx )} (1.1.1) ∗ Corresponding author. E-mail addresses: mhimdad@yahoo.co.in (M. Imdad), k ladlay@yahoo.com (L. Khan). 0362-546X/$ - see front matter c  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2006.09.037