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 Generalized Contractive Hybrid Pairs in Symmetric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 869407 11 pages doi 2009 869407 Research Article Common Fixed Points of Generalized Contractive Hybrid Pairs in Symmetric Spaces Mujahid Abbas1 and Abdul Rahim Khan2 1 Centre for Advanced Studies in Mathematics and Department of Mathematics Lahore University of Management Sciences 54792 Lahore Pakistan 2 Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Correspondence should be addressed to Abdul Rahim Khan arahim@ Received 16 April 2009 Revised 23 July 2009 Accepted 10 November 2009 Recommended by Jerzy Jezierski Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps satisfying generalized contractive conditions are established in a symmetric space. Copyright 2009 M. Abbas and A. R. Khan. 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 In 1968 Kannan 1 proved a fixed point theorem for a map satisfying a contractive condition that did not require continuity at each point. This paper was a genesis for a multitude of fixed point papers over the next two decades. Sessa 2 coined the term weakly commuting maps. Jungck 3 generalized the notion of weak commutativity by introducing compatible maps and then weakly compatible maps 4 . Al-Thagafi and Shahzad 5 gave a definition which is proper generalization of nontrivial weakly compatible maps which have coincidence points. Jungck and Rhoades 6 studied fixed point results for occasionally weakly compatible owe maps. Recently Zhang 7 obtained common fixed point theorems for some new generalized contractive type mappings. Abbas and Rhoades 8 obtained common fixed point theorems for hybrid pairs of .