Common fixed point and invariant approximation results
Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 537-545 Printed September 1, 2007
Mujahid Abbas and Jong Kyu Kim Indiana University, Kyungnam University
Abstract : Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in the setup of certain metrizable topological vector spaces are obtained. As applications, related results on best approximation are derived. Our results extend, generalize and unify various known results in the literature.
Keywords : metrizable topological vector space, common fixed point, uniformly $R$-subweakly commuting mapping, asymptotically $S$-nonexpansive mapping, best approximation.