Opuscula Math. 31, no. 1 (2011), 5-14

Opuscula Mathematica

A Meir-Keeler type common fixed point theorem for four mappings

Mohamed Akkouchi

Abstract. In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result generalizes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly compatibility property and replacing the completeness of the space with a set of four alternative conditions for maps satisfying an implicit relation. Also, our result improves the main result of H. Bouhadjera, A. Djoudi.

Keywords: common fixed point for four mappings, weakly compatible mappings, Meir-Keeler type contractive condition, complete metric spaces.

Mathematics Subject Classification: 54H25, 47H10.

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  • Mohamed Akkouchi
  • Université Cadi Ayyad, Faculté des Sciences-Semlalia, Département de Mathématiques, Av. Prince My Abdellah, BP. 2390, Marrakech Maroc (Morocco)
  • Received: 2010-04-09.
  • Revised: 2010-06-18.
  • Accepted: 2010-06-19.
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Cite this article as:
Mohamed Akkouchi, A Meir-Keeler type common fixed point theorem for four mappings, Opuscula Math. 31, no. 1 (2011), 5-14, http://dx.doi.org/10.7494/OpMath.2011.31.1.5

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