Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 898109, 14 pages
Research Article

Coincidence Theorems for Certain Classes of Hybrid Contractions

Department of Mathematics, School of Mathematical & Computational Sciences, Walter Sisulu University, Nelson Mandela Drive Mthatha 5117, South Africa

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.