Some Stability Results in Metric Trees

Some Stability Results in Metric Trees

In this lecture, we introduce the concept of the stable fixed point property for mappings, and we prove the existence of the stable fixed point property for continuous mappings defined on a compact and convex subset of a complete metric tree. Also, inspired of the Kirkʹs proof of the fixed point property for continuous mappings in complete metric trees, we generalize some theorems in such spaces.