Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition | De la Sen and Agarwal Fixed Point Theory and Applications 2011 2011 59 http content 2011 1 59 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition M De la Sen 1 and Ravi P Agarwal2 Correspondence manuel. delasen@ 1Instituto de Investigacion y Desarrollo de Procesos Universidad del Pais Vasco Campus of Leioa Bizkaia Aptdo. 644-Bilbao 48080-Bilbao Spain Full list of author information is available at the end of the article Springer Abstract This article discusses a more general contractive condition for a class of extended p 2 -cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. If the space is uniformly convex and the subsets are nonempty closed and convex then all the iterates converge to a unique closed limiting finite sequence which contains the best proximity points of adjacent subsets and reduces to a unique fixed point if all such subsets intersect. 1. Introduction A general contractive condition of rational type has been proposed in 1 2 for a partially ordered metric space. Results about the existence of a fixed point and then its uniqueness under supplementary conditions are proved in those articles. The general rational contractive condition of 3 includes as particular cases several of the existing ones 1 4-12 including Banach s principle 5 and Kannan s fixed point theorems 4 8 9 11 . The general rational contractive conditions of 1 2 are applicable only on distinct points of the considered metric spaces. In particular the fixed point theory for Kannan s mappings is extended in 4 by the use of a non-increasing function affecting to the contractive condition and the best constant to ensure that a fixed point is also obtained. Three fixed point .
