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The Scientific World Journal
Volume 2014 (2014), Article ID 585964, 14 pages
Research Article

Fixed Point Results for --Contractive Maps with Application to Boundary Value Problems

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
3Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Received 9 March 2014; Accepted 29 March 2014; Published 7 May 2014

Academic Editor: M. Mursaleen

Copyright © 2014 Nawab Hussain 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.


We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.