MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Common fixed points of commuting mappings in ultrametric spaces
Zahra Alinejad and Alireza Kamel Mirmostafaee

Abstract

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

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Keywords: Contraction mapping; fixed point; non-Archimedean metric space.

MSC: 47H10, 47H09, 54E35

Pages:  204--214     

Volume  68 ,  Issue  3 ,  2016