An effective metric on C(H,K) with normal structure

TL;DR

This paper introduces a new metric with normal structure on C(H,K) and develops fixed point theorems for non-expansive maps, showing bounded orbits imply fixed points for automorphism groups.

Contribution

It proposes a novel metric with normal structure on C(H,K) and a technique to establish fixed points for non-expansive maps in this setting.

Findings

Presence of bounded orbit implies fixed point existence.

Fixed point theorems for groups of h-biholomorphic automorphisms.

New metric with normal structure on C(H,K)

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).