The Mann algorithm in a complete geodesic space with curvature bounded above

Abstract

The purpose of this paper is to prove two Δ-convergence theorems of the Mann algorithm to a common fixed point for a countable family of mappings in the case of a complete geodesic space with curvature bounded above by a positive number. The first one for nonexpansive mappings improves the recent result of He et al. (Nonlinear Anal. 75:445-452, 2012). The last one is proved for quasi-nonexpansive mappings and applied to the problem of finding a common fixed point of a countable family of quasi-nonexpansive mappings. ©2013 Kimura et al.; licensee Springer.