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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 967132, 9 pages
http://dx.doi.org/10.1155/2013/967132
Research Article

Some Fixed Point Theorems in -Metric Space Endowed with Graph

1Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Sector, H-12, Islamabad, Pakistan
2Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
3Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Received 6 July 2013; Revised 5 September 2013; Accepted 6 September 2013

Academic Editor: Douglas Anderson

Copyright © 2013 Maria Samreen 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.

Abstract

We define some notions of contraction mappings in -metric space endowed with a graph and subsequently establish some fixed point results for such classes of contractions. According to the applications of our results, we obtain fixed point theorems for cyclic operators and an existence theorem for the solution of an integral equation.