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math.FA2019
Compact and Limited Operators
Mohammed Bachir, Gonzalo Flores, Sebastián Tapia-García
Let be a bounded linear operator between two normed spaces. We characterize compactness of in terms of differentiability of the Lipschitz functions defined on wi…
math.FA2019
Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
Nazaret Bruno, Mohammed Bachir, Bruno Nazaret
Schweizer, Sklar and Thorp proved in 1960 that a Menger space under a continuous -norm , induce a natural topology wich is metrizable. We extend this result to…
math.FA2019
Probabilistic Arzela-Ascoli theorem
Mohammed Bachir, Nazaret Bruno
We prove that, in the space of all probabilistic continuous functions from a probabilistic metric space G to the set + of all cumulative distribution functions vanishing at 0,…