Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem - Archive ouverte HAL Access content directly
Journal Articles Topology and its Applications Year : 2021

Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem

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Abstract

This work is devoted to the metrization of probabilistic spaces. More precisely, given such a space $(G,D,\star)$ and provided that the triangle function $\star$ is continuous, we exhibit an explicit and canonical metric $\sigma_D$ on $G$ such that the associated topology is homeomorphic to the so-called strong topology. As applications, we make advantage of this explicit metric to present some fixed point theorems on such probabilistic metric structures and we prove a probabilistic version of the Arzela-Ascoli theorem.
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Dates and versions

hal-03075552 , version 1 (16-12-2020)

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  • HAL Id : hal-03075552 , version 1

Cite

Mohammed Bachir, Nazaret Bruno. Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem. Topology and its Applications, 2021, 289. ⟨hal-03075552⟩
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