Mizoguchi-Takahashi local contractions to Feng-Liu contractions

• Maiti, Pallab ^[1] ; Sultana, Asrifa ^[1]
  1. [1] Indian Institute of Technology Bhilai
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 2, 2024, págs. 321-329
• Idioma: inglés
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• Resumen

  • In this article, we establish that any uniformly local Mizoguchi-Takahashi contraction is actually a set-valued contraction due to Feng and Liu on a metrically convex complete metric space. Through an example, we demonstrate that this result need not hold on any arbitrary metric space. Furthermore, when the metric space is compact, we derive that any Mizoguchi-Takahashi local contraction and Nadler local contraction are equivalent. Moreover, a result related to invariant best approximation is established.