Freely quasiconformal and locally weakly quasisymmetric mappings in metric spaces

Abstract In this article, we investigate the relationship between freely quasiconformal mappings and locally weakly quasisymmetric mappings in quasiconvex and complete metric spaces. We first prove the equivalence of freely quasiconformal mappings, ring properties, and locally weakly quasisymmetric mappings. Finally, we prove that the composition of two locally weakly quasisymmetric mappings in metric spaces is locally weakly quasisymmetric mapping.