Lipschitz isomorphism and fixed point theorem for normed groups

Abstract This paper aims to propose normed structures for groups and to establish the Lipschitz mapping of a normed group to itself. We also investigate some conjugate and isomorphic Lipschitz mappings to determine the equivalent norm and inverse Lipschitz mappings. Specifically, in the main result, we present a fixed point theorem for self-mappings satisfying certain contraction principles on a complete normed group.