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

Hector Andres Granada Diaz; Simeon Casanova Trujillo; Fredy E. Hoyos

doi:10.3390/math10193559

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arXiv · 2601.06130

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

Hector Andres Granada Diaz·Simeon Casanova Trujillo·Fredy E. Hoyos

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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

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Hector Andres Granada Diaz, Simeon Casanova Trujillo, Fredy E. Hoyos. 2026-01-04. Derivative for Functions $f : G \to H$, Where $G$ Is a Metric Divisible Group. https://doi.org/10.3390/math10193559

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