The canonical partial metric and the uniform convexity on normed spaces

Sandra Oltra; Salvador Romaguera; E. A. Sánchez-Pérez

doi:10.4995/agt.2005.1954

Authors

Sandra Oltra Universitat Politècnica de València
Salvador Romaguera Universitat Politècnica de València
E. A. Sánchez-Pérez Universitat Politècnica de València

DOI:

https://doi.org/10.4995/agt.2005.1954

Keywords:

Partial metric, Convexity, Normed spaces

Abstract

In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm.

We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.

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Author Biographies

Sandra Oltra, Universitat Politècnica de València

Departamento de Matemática Aplicada

Salvador Romaguera, Universitat Politècnica de València

Departamento de Matemática Aplicada

E. A. Sánchez-Pérez, Universitat Politècnica de València

Departamento de Matemática Aplicada

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