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A fixed point of generalized T F -contraction mappings in cone metric spaces

Farshid Khojasteh1*, Abdolrahman Razani1 and Sirous Moradi2

Author Affiliations

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran

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Fixed Point Theory and Applications 2011, 2011:14  doi:10.1186/1687-1812-2011-14

Published: 8 July 2011

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.

Keywords:
integral type contraction; regular cone; Meir-Keeler contraction; TF-contraction; -function