Krasnoselskii-Mann Method for Multi-valued Non-Self Mappings in CAT(0) Spaces

Abstract

We define Mann iterative scheme in CAT(0) spaces and obtain $\triangle$-convergence and strong convergence of the iterative scheme to a fixed point of multi-valued non-self nonexpansive mappings. We also obtain strong convergence of the scheme to a fixed point of multi-valued non-self quasi-nonexpansive mappings with appropriate conditions.
Our theorems improve and unify most
of the results that have been proved for this important class of
nonlinear operators.