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The Scientific World Journal
Volume 2013, Article ID 194897, 8 pages
Research Article

Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces

1Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad 44000, Pakistan

Received 30 April 2013; Accepted 18 June 2013

Academic Editors: A. Bekir, A. Ibeas, and A. M. Peralta

Copyright © 2013 Abdullah Shoaib 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.


Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results.