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: Research Article Fixed Point Theorems for n Times Reasonable Expansive Mapping | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 302617 6 pages doi 2008 302617 Research Article Fixed Point Theorems for n Times Reasonable Expansive Mapping Chunfang Chen and Chuanxi Zhu Institute of Mathematics Nanchang University Nanchang Jiangxi 330031 China Correspondence should be addressed to Chuanxi Zhu chuanxizhu@ Received 29 February 2008 Revised 3 May 2008 Accepted 16 August 2008 Recommended by Jerzy Jezierski Based on previous notions of expansive mapping n times reasonable expansive mapping is defined. The existence of fixed point for n times reasonable expansive mapping is discussed and some new results are obtained. Copyright 2008 C. Chen and C. Zhu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and preliminaries The research about fixed points of expansive mapping was initiated by Machuca see 1 . Later Jungck discussed fixed points for other forms of expansive mapping see 2 . In 1982 Wang et al. see 3 published a paper in Advances in Mathematics about expansive mapping which draws great attention of other scholars. Also Zhang has done considerable work in this field. In order to generalize the results about fixed point theory Zhang see 4 published his work Fixed Point Theory and Its Applications in which the fixed point problem for expansive mapping is systematically presented in a chapter. As applications he also investigated the existence of solutions of equations for locally condensing mapping and locally accretive mapping. In 1991 based on the results obtained by others the author defined several new kinds of expansive-type mappings in 5 which expanded the expansive-type mapping from 19 to 23 and gave some new applications. Recently the study about fixed point theorem for expansive mapping and nonexpansive .
