A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications

• Autores: Gonzalo García
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 1, 2019, págs. 265-279
• Idioma: inglés
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• Resumen

  • We present a novel result that, in certain sense, generalizes the Arzelà-Ascoli theorem. Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but can be used as an alternative tool in certain fixed problems problems where such measures do not work out. To justify our results, we will analyze the existence of (continuous) solutions of certain Volterra integral equations defined by vector valued functions.