Strong convergence theorems for multivalued mappings in a geodesic space with curvature bounded above

Abstract

We prove two strong convergence results of the Ishikawa iteration for a multivalued quasi-nonexpansive mapping in a complete geodesic space with curvature bounded above. Our results improve significantly the recent results of Panyanak (Fixed Point Theory Appl. 2014:1, 2014) in the sense that many restrictions in his results are weakened. In particular, we can conclude that the convergence result of the Mann iteration which cannot be deduced from Panyanak’s results.