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Journal of Function Spaces
Volume 2016 (2016), Article ID 6514920, 7 pages
http://dx.doi.org/10.1155/2016/6514920
Research Article

Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Sargodha (Subcampus Bhakkar), Bhakkar, Pakistan

Received 9 April 2016; Revised 27 June 2016; Accepted 28 June 2016

Academic Editor: Adrian Petrusel

Copyright © 2016 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.

Abstract

Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi -contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in -chainable metric space are also discussed.