Discontinuity at fixed point and metric completeness

• Bisht, Ravindra K. ^[1] ; Rakocevic, Vladimir ^[2]
  1. [1] National Defence Academy

     National Defence Academy

     India

     
  2. [2] University of Nis

     University of Nis

     Serbia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 21, Nº. 2, 2020, págs. 349-362
• Idioma: inglés
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• Resumen

  • In this paper, we prove some new fixed point theorems for a generalized class of Meir-Keeler type mappings, which give some new solutions to the Rhoades open problem regarding the existence of contractive mappings that admit discontinuity at the fixed point. In addition to it, we prove that our theorems characterize completeness of the metric space as well as Cantor's intersection property.