Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Some fixed point theorems for contractive multivalued mappings induced by generalized distance in metric spaces | Hirunworakit and Petrot Fixed Point Theory and Applications 2011 2011 78 http content 2011 1 78 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Some fixed point theorems for contractive multivalued mappings induced by generalized distance in metric spaces Soawapak Hirunworakit 1 and Narin Petrot1 2 Correspondence narinp@ department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Full list of author information is available at the end of the article Springer Abstract The purpose of this paper is to prove some existence theorems for fixed point problem by using a generalization of metric distance namely u-distance. Consequently some special cases are discussed and an interesting example is also provided. Presented results are generalizations of the important results due to Ume Fixed Point Theory Appl 2010 397150 21 pp 2010 and Suzuki and Takahashi Topol Methods Nonlinear Anal 8 371-382 1996 . 2010 Mathematics Subject Classification 47H09 47H10. Keywords complete metric space generalized multi-valued contractive u-distance fixed point. 1. Introduction and preliminaries Let X d be a metric space. A mapping T X X is said to be contraction if there exists r e 0 1 such that d T x T y rd x y Yx y e X. In 1922 Banach 1 proved that if X d is a complete metric space and the mapping T satisfies then T has a unique fixed point that is T u u for some u e X. Such a result is well known and called the Banach contraction mapping principle. Following the Banach contraction principle Nadler Jr. 2 established the fixed point result for multi-valued contraction maps which in turn is a generalization of the Banach contraction principle. Since then there are several extensions and generalizations of these two important principles see 3 4 and 5-11 for examples. In 1996 Kada et al. 4 introduced the concept of w-distance on a metric space X d . By using such a w-distance
