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: FIXED POINT THEORY ON EXTENSION-TYPE SPACES AND ESSENTIAL MAPS ON TOPOLOGICAL SPACES | FIXED POINT THEORY ON EXTENSION-TYPE SPACES AND ESSENTIAL MAPS ON TOPOLOGICAL SPACES DONAL O REGAN Received 19 November 2003 We present several new fixed point results for admissible self-maps in extension-type spaces. We also discuss a continuation-type theorem for maps between topological spaces. 1. Introduction In Section 2 we begin by presenting most of the up-to-date results in the literature 3 5 6 7 8 12 concerning fixed point theory in extension-type spaces. These results are then used to obtain a number of new fixed point theorems one concerning approximate neighborhood extension spaces and another concerning inward-type maps in extensiontype spaces. Our first result was motivated by ideas in 12 whereas the second result is based on an argument of Ben-El-Mechaiekh and Kryszewski 9 . Also in Section 2 we present a new continuation theorem for maps defined between Hausdorff topological spaces and our theorem improves results in 3 . For the remainder of this section we present some definitions and known results which will be needed throughout this paper. Suppose X and Y are topological spaces. Given a class of maps X X Y denotes the set of maps F X 2Y nonempty subsets of Y belonging to and ỵc the set of finite compositions of maps in X. We let w Z FixF 0VF e A Z Z where FixF denotes the set of fixed points of F. The class A of maps is defined by the following properties i A contains the class of single-valued continuous functions ii each F e Ac is upper semicontinuous and closed valued iii Bn e Ac for all n e 1 2 . here Bn x e Rn xh 1 . Remark . The class A is essentially due to Ben-El-Mechaiekh and Deguire 7 . It includes the class of maps A of Park A is the class of maps defined by i iii and iv each F e Ac is upper semicontinuous and compact valued . Thus if each F e Ac is compact Copyright 2004 Hindawi Publishing Corporation Fixed Point Theory and Applications 2004 1 2004 13-20 2000 Mathematics Subject Classification 47H10 URL http
