Communications of the
Korean Mathematical Society CKMS

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee \cite{lee} from the closed convex subset of a convex cone metric space to whole space.

Keywords: convex metric spaces, cone metric spaces, asymptotically quasi-nonexpansive mappings, common fixed point, strong convergence

MSC numbers: 47H05, 47H09, 47H17, 49J40