integral type contraction, regular cone, Meir-Keeler contraction, TF -contraction, -function, Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433

Abstract In this paper, the existence of a fixed point for TF -contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X → X is a one to one and closed graph function and F : P → P is non-decreasing and right continuous, with F -1(0) = -0} and F(tn ) → 0 implies tn → 0. Our results, extend previous results given by Meir and Keeler (J. Math. Anal. Appl. 28, 326-329, 1969), Branciari (Int. J. Math. sci. 29, 531-536, 2002), Suzuki (J. Math. Math. Sci. 2007), Rezapour et al. (J. Math. Anal. Appl. 345, 719-724, 2010), Moradi et al. (Iran. J. Math. Sci. Inf. 5, 25-32, 2010) and Khojasteh et al. (Fixed Point Theory Appl. 2010). MSC(2000): 47H10; 54H25; 28B05.