tailieunhanh - Báo cáo hóa học: " FIXED POINT THEORY ON EXTENSION-TYPE SPACES AND ESSENTIAL MAPS ON TOPOLOGICAL 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: 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