Opuscula Math. 31, no. 1 (2011), 5-14
A Meir-Keeler type common fixed point theorem for four mappings
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.
- Received: 2010-04-09.
- Revised: 2010-06-18.
- Accepted: 2010-06-19.