Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A fixed point of generalized TF-contraction mappings in cone metric spaces | Khojasteh et al. Fixed Point Theory and Applications 2011 2011 14 http content 2011 1 14 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access A fixed point of generalized Tf-contraction mappings in cone metric spaces Farshid Khojasteh 1 Abdolrahman Razani1 and Sirous Moradi2 Correspondence fr_khojasteh@ department of Mathematics Science and Research Branch Islamic Azad University Tehran Iran Full list of author information is available at the end of the article SpringerOpen0 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-con-traction L-function 1 Introduction In 2007 Huang et al. 1 introduced the cone metric spaces and proved some fixed point theorems. Recently Many results closely related to cone metric spaces are given see 2-6 . In addition some topological properties of these spaces are surveyed. In 2010 Khojasteh et al. 7 introduced a new concept of integral with respect to a cone and proved some fixed point theorems in cone metric spaces. At the same year Moradi et al. 8 introduced a new type of fixed point theorem by defining Tf-contrac-tion as a new contractive condition in complete metric spaces. To state this result some preliminaries from 8 9 are recalled. First set R0 0 rc and F R0 R0 F is non - decreasing right .
