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Báo cáo hóa học: "COINCIDENCE AND FIXED POINT THEOREMS FOR FUNCTIONS IN S-KKM CLASS ON GENERALIZED CONVEX SPACES"

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: COINCIDENCE AND FIXED POINT THEOREMS FOR FUNCTIONS IN S-KKM CLASS ON GENERALIZED CONVEX SPACES | COINCIDENCE AND FIXED POINT THEOREMS FOR FUNCTIONS IN S-KKM CLASS ON GENERALIZED CONVEX SPACES TIAN-YUAN KUO YOUNG-YE HUANG JYH-CHUNG JENG AND CHEN-YUH SHIH Received 25 October 2004 Revised 13 July 2005 Accepted 1 September 2005 We establish a coincidence theorem in S-KKM class by means of the basic defining property for multifunctions in S-KKM. Based on this coincidence theorem we deduce some useful corollaries and investigate the fixed point problem on uniform spaces. Copyright 2006 Tian-Yuan Kuo et al. 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 A multimap T X 2Y is a function from a set X into the power set 2Y of Y. If H T X 2Y then the coincidence problem for H and T is concerned with conditions which guarantee that H x n T x 0 for some x e X. Park 11 established a very general coincidence theorem in the class Uịí of admissible functions which extends and improves many results of Browder 1 2 Granas and Liu 6 . On the other hand Huang together with Chang et al. 3 introduced the S-KKM class which is much larger than the class Uịí. A lot of interesting and generalized results about fixed point theory on locally convex topological vector spaces have been studied in the setting of S-KKM class in 3 . In this paper we will at first construct a coincidence theorem in S-KKM class on generalized convex spaces by means of the basic defining property for multimaps in S-KKM class. And then based on this coincidence theorem we deduce some useful corollaries and investigate the fixed point problem on uniform spaces. 2. Preliminaries Throughout this paper Y denotes the class of all nonempty finite subsets of a nonempty set Y. The notation T X Y stands for a multimap from a set X into 2Y 0 . For a multimap T X 2Y the following notations are used a T A UxcaT x for A Q X b T- y x e X y e T x for y e