Bulletin of the
Korean Mathematical Society BKMS

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.

MSC numbers: 47H09, 47H10, 47H19, 54H25