This is an announcement for the paper “An effective metric on $C(H,K)$ with normal structure” by Mona Nabiei.
Abstract: This study first defines a new metric with normal structure on $C(H,K)$ and then a new technique to prove fixed point theorems for families of non-expansive maps on this metric space. Indeed, it shows that the presence of a bounded orbit implies the existence of a fixed point for a group of h-biholomorphic automorphisms on $C(H,K)$.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04015