Common fixed points of commuting mappings in ultrametric spaces

Authors

  • Zahra Alinejad Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Mashhad, Iran Author
  • Alireza Kamel Mirmostafaee Center of Excellence in Analysis on Algebraic Structures, Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Mashhad, Iran Author

Keywords:

Contraction mapping, fixed point, non-Archimedean metric space

Subjects:

47H10, 47H09, 54E35

Abstract

In this paper, we will use implicit functions toobtain a general result about the existence of a unique commonfixed point for commuting mappings in ultrametric spaces. Thisresult enables us to improve some known fixed point theorems andenables us to obtain a relation between completeness and theexistence of a unique fixed point for self-mappings innon-Archimedean metric spaces. By presenting some counterexamples,we will show that our results cannot be extended to general metricspaces.

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Published

2016-07-15

Issue

Vol. 68 No. 3 (2016): Vol. 68, Issue 3

Section

Articles

License

Copyright (c) 2016 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.