Common fixed-point results in uniformly convex Banach spaces

Abstract

We introduce a condition on mappings, namely condition (K). In a uniformly convex Banach space, the condition is weaker than quasi-nonexpansiveness and weaker than asymptotic nonexpansiveness. We also present the existence theorem of common fixed points for a commuting pair consisting of a mapping satisfying condition (K) and a multivalued mapping satisfying conditions (E) and (Cλ) for some λ ∈ (0, 1). © 2012 Akkasriworn et al.; licensee Springer.