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 Coincidence Theorems for Certain Classes of Hybrid Contractio | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 898109 14 pages doi 2010 898109 Research Article Coincidence Theorems for Certain Classes of Hybrid Contractions S. L. Singh and S. N. Mishra Department of Mathematics School of Mathematical Computational Sciences Walter Sisulu University Nelson Mandela Drive Mthatha 5117 South Africa Correspondence should be addressed to S. N. Mishra smishra@ Received 27 August 2009 Accepted 9 October 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 S. L. Singh and S. N. Mishra. 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. Coincidence and fixed point theorems for a new class of hybrid contractions consisting of a pair of single-valued and multivalued maps on an arbitrary nonempty set with values in a metric space are proved. In addition the existence of a common solution for certain class of functional equations arising in dynamic programming under much weaker conditions are discussed. The results obtained here in generalize many well known results. 1. Introduction Nadler s multivalued contraction theorem 1 see also Covitz and Nadler Jr. 2 was subsequently generalized among others by Reich 3 and Ciric 4 . For a fundamental development of fixed point theory for multivalued maps one may refer to Rus 5 . Hybrid contractive conditions that is contractive conditions involving single-valued and multivalued maps are the further addition to metric fixed point theory and its applications. For a comprehensive survey of fundamental development of hybrid contractions and historical remarks refer to Singh and Mishra 6 see also Naimpally et al. 7 and Singh and Mishra 8 . Recently Suzuki 9 Theorem 2 obtained a forceful generalization of the classical Banach contraction theorem in a remarkable way. Its further outcomes by .