Derivative for Functions $f : G \to H$, Where $G$ Is a Metric Divisible Group

TL;DR

This paper introduces a derivative concept for functions between metric divisible groups and metric Abelian groups, establishing fundamental differentiation theorems including the Chain Rule.

Contribution

It defines a new derivative for functions on metric divisible groups and proves basic calculus theorems in this setting, extending classical analysis.

Findings

Defined a derivative for functions between metric divisible and Abelian groups

Established the Chain Rule in this new context

Proved fundamental differentiation theorems

Abstract

In this paper, a derivative for functions $f : G \to H$, where $G$ is any metric divisible group and $H$ is a metric Abelian group with a group metric, is defined. Basic differentiation theorems are stated and demonstrated. In particular, we obtain the Chain Rule