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Journal of Function Spaces
Volume 2016, Article ID 3690421, 10 pages
Research Article

On the Existence of Coincidence and Common Fixed Point of Two Rational Type Contractions and an Application in Dynamical Programming

1Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
2Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt

Received 29 March 2016; Revised 23 May 2016; Accepted 12 June 2016

Academic Editor: Pasquale Vetro

Copyright © 2016 Ahmed H. Soliman and Tamer Nabil. 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.


We establish some coincidence point results for self-mappings satisfying rational type contractions in a generalized metric space. Presented coincidence point theorems weaken and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results apply, in particular, to the study of solvability of functional equations arising in dynamic programming.