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Bull. Korean Math. Soc. 2008; 45(4): 671-680
Printed December 1, 2008
Copyright © The Korean Mathematical Society.
Common fixed point and invariant approximation in Menger convex metric spaces
Nawab Hussain, Mujahid Abbas, and Jong Kyu Kim
King Abdul Aziz University, Indiana University, and Kyungnam University
Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.
Keywords: convex metric space, common fixed point, uniformly $C_{q}$-commuting mapping, asymptotically $S$-nonexpansive mapping, best approximation
MSC numbers: 47H09, 47H10, 47H19, 54H25
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