Acta Mathematica Scientia 2012,32B(6):2119–2130 http://actams.wipm.ac.cn MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS ∗ Hassen Aydi Universit´ e de Monastir, Institut Sup´ erieur d’Informatique de Mahdia, Route de R´ ejiche, Km 4, BP 35, Mahdia 5121, Tunisie E-mail: hassen.aydi@isima.rnu.tn Erdal Karapınar Department of Mathematics, Atilim University 06836, ˙ Incek, Ankara, Turkey E-mail: erdalkarapinar@yahoo.com; ekarapinar@atilim.edu.tr Calogero Vetro Dipartimento di Matematica e Informatica, Universit` a di Palermo, Via Archirafi 34, 90123 Palermo, Italy E-mail: cvetro@math.unipa.it Abstract In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction. Key words tripled fixed point theorems; Meir-Keeler type contractions; partially or- dered sets 2010 MR Subject Classification 47H10; 54H25 1 Introduction and Preliminaries In this paper, we consider partially ordered metric spaces and discuss existence and unique- ness of some tripled fixed points on this class by using Meir-Keeler type contractions. The exis- tence of fixed points in partially ordered metric spaces was considered first by Ran and Reurings [14] in 2004. Later on, Nieto and Lopez [12] announced some more results on partially ordered metric spaces. Recently, some theorems of existence and uniqueness were reported on partially ordered complete metric spaces (see, e.g. [1, 2, 5, 9, 11,12, 14]). In 1965, Presi´ c [13] introduced the notion of coupled fixed point. Successively, Bhaskar and Lakshmikantham in [5] proved theorems of existence and uniqueness of coupled fixed point. After this, Lakshmikantham and ´ Ciri´ c in [9] extended the results in [5] by using mixed g- monotone property. Since then many authors have worked on coupled fixed point theorems (see e.g. [3, 4, 6–10]). In particular, Samet [15] defined generalized Meir-Keeler type functions * Received July 27, 2011; revised December 2, 2011. C. Vetro is supported by Universit`a degli Studi di Padermo, Local Project R. S. ex 60\char37.