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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 456482, 13 pages
http://dx.doi.org/10.1155/2014/456482
Research Article

Discussions on Recent Results for - -Contractive Mappings

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
3Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran

Received 17 December 2013; Accepted 12 January 2014; Published 2 March 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 N. 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

We establish certain fixed point results for -generalized convex contractions, -weakly Zamfirescu mappings, and -Ćirić strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.