A Note on Common Fixed Point Results in Uniformly Convex Hyperbolic Spaces

Abstract

It is shown that the notion of mappings satisfying condition(K)introduced by Akkasriworn et al. (2012) is weaker than the notion of asymptotically quasi-nonexpansive mappings in the sense of Qihou (2001) and is weaker than the notion of pointwise asymptotically nonexpansive mappings in the sense of Kirk and Xu (2008). We also obtain a common fixed point for a commuting pair of a mapping satisfying condition(K)and a multivalued mapping satisfying condition(Cλ)for someλ∈(0,1). Our results properly contain the results of Abkar and Eslamian (2012), Akkasriworn et al. (2012), and many others.