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 Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 746045 15 pages doi 2010 746045 Research Article Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces M. H. Shah 1 N. Hussain 2 and A. R. Khan3 1 Department of Mathematical Sciences LUMS DHA Lahore Pakistan 2 Department of Mathematics King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia 3 Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Correspondence should be addressed to A. R. Khan arahim@ Received 17 May 2010 Accepted 21 July 2010 Academic Editor Yeol J. E. Cho Copyright 2010 M. H. Shah 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. Using the notion of weakly F-contractive mappings we prove several new common fixed point theorems for commuting as well as noncommuting mappings on a topological space X. By analogy we obtain a common fixed point theorem of mappings which are strongly F-expansive on X. 1. Introduction It is well known that if X is a compact metric space and f X X is a weakly contractive mapping see Section 2 for the definition then f has a fixed point in X see 1 p. 17 . In late sixties Furi and Vignoli 2 extended this result to a-condensing mappings acting on a bounded complete metric space see 3 for the definition . A generalized version of Furi-Vignoli s theorem using the notion of weakly F-contractive mappings acting on a topological space was proved in 4 see also 5 . On the other hand in 6 while examining KKM maps the authors introduced a new concept of lower upper semicontinuous function see Definition Section 2 which is more general than the classical one. In 7 the authors used this definition of lower semicontinuity to redefine weakly .
