Derivative for Functions f: G → H, Where G Is a Metric Divisible Group

Héctor Andrés Granada Díaz, Simeón Casanova Trujillo () and Fredy E. Hoyos
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Héctor Andrés Granada Díaz: Departamento de Matemáticas y Estadística, Universidad del Tolima, Grupo de Matemáticas del Tolima (Grupo-MaT), Barrio Santa Helena Parte Alta Cl 42 1-02, Ibagué 730006299, Colombia
Simeón Casanova Trujillo: Grupo de Investigación Cálculo Científico y Modelamiento Matemático, Universidad Nacional de Colombia, Sede Manizales, Manizales 170003, Colombia
Fredy E. Hoyos: Departamento de Energía Eléctrica y Automática, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, Colombia

Mathematics, 2022, vol. 10, issue 19, 1-10

Abstract: In this paper, a derivative for functions f : G → 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 Role.

Keywords: topological group; homomorphism; differentiability; metric group; locally compact space; topological vector space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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