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Báo cáo hóa học: " The existence of fixed points for new nonlinear multivalued maps and their applications"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : The existence of fixed points for new nonlinear multivalued maps and their applications | He et al. Fixed Point Theory and Applications 2011 2011 84 http www.fixedpointtheoryandapplications.eom content 2011 1 84 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access The existence of fixed points for new nonlinear multivalued maps and their applications Zhenhua He1 Wei-Shih Du2 and Ing-Jer Lin2 Correspondence wsdu@nknucc. nknu.edu.tw 2Department of Mathematics National Kaohsiung Normal University Kaohsiung 824 Taiwan Full list of author information is available at the end of the article Springer Abstract In this paper we first establish some new fixed point theorems for MT -functions. By using these results we can obtain some generalizations of Kannan s fixed point theorem and Chatterjea s fixed point theorem for nonlinear multivalued contractive maps in complete metric spaces. Our results generalize and improve some main results in the literature and references therein. Mathematics Subject Classifications 47H10 54H25 Keywords T T -function MT-function function of contractive factor Kannan s fixed point theorem Chat-terjea s fixed point theorem 1. Introduction Throughout this paper we denote by N and R the sets of positive integers and real numbers respectively. Let X d be a metric space. For each x e X and A X let d x A infy e A d x y . Let CB X be the family of all nonempty closed and bounded subsets of X. A function H CB X X CB X 0 to defined by H A B max sup d x A sup d x B xeB xeB is said to be the Hausdorff metric on CB X induced by the metric d on X. A point x in X is a fixed point of a map T if Tx x when T X X is a single-valued map or x e Tx when T X 2X is a multivalued map . The set of fixed points of T is denoted by F t . It is known that many metric fixed point theorems were motivated from the Banach contraction principle see e.g. 1 that plays an important role in various fields of applied mathematical analysis. Later Kannan 2 3 and Chatterjea 4 established the following fixed point theorems. Theorem K. Kannan 2 3 Let