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On Completeness in Metric Spaces and Fixed Point Theorems

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Abstract

Complete ultrametric spaces constitute a particular class of the so called, recently, G-complete metric spaces. In this paper we characterize a more general class called weak G-complete metric spaces, by means of nested sequences of closed sets. Then, we also state a general fixed point theorem for a self-mapping of a weak G-complete metric space. As a corollary, every asymptotically regular self-mapping of a weak G-Complete metric space has a fixed point.

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Authors and Affiliations

  1. Instituto de Investigación para la Gestión Integrada de Zonas Costeras, Universitat Politècnica de València, Campus de Gandia Calle Paranimf 1, 46730, Gandia, Spain

    Valentín Gregori, Bernardino Roig & Almanzor Sapena

  2. Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, Carretera de Valldemossa km. 7.5, 07122, Palma, Spain

    Juan-José Miñana

Authors
  1. Valentín Gregori
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  2. Juan-José Miñana
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  3. Bernardino Roig
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  4. Almanzor Sapena
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Corresponding author

Correspondence to Juan-José Miñana.

Additional information

V. Gregori acknowledges the support of the Ministry of Economy and Competitiveness of Spain under Grant MTM2015-64373-P (MINECO/Feder, UE). J.J. Miñana acknowledges financial support from the Spanish Ministry of Economy and Competitiveness under Grants TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds, by Programa Operatiu FEDER 2014–2020 de les Illes Balears, by Project Ref. PROCOE/4/2017 (Direcció General d’Innovació i Recerca, Govern de les Illes Balears), and by project ROBINS. The latter has received research funding from the EU H2020 framework under GA 779776. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.

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Gregori, V., Miñana, JJ., Roig, B. et al. On Completeness in Metric Spaces and Fixed Point Theorems. Results Math 73, 142 (2018). https://doi.org/10.1007/s00025-018-0896-4

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  • DOI: https://doi.org/10.1007/s00025-018-0896-4

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