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Abstract and Applied Analysis
Volume 2014, Article ID 985080, 10 pages
http://dx.doi.org/10.1155/2014/985080
Research Article

The Generalized Weaker -Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

1Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Applied Mathematics, National Hsinchu University of Education, Taiwan
3Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
4Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia

Received 6 February 2014; Accepted 7 May 2014; Published 26 May 2014

Academic Editor: Qamrul Hasan Ansari

Copyright © 2014 Maryam A. Alghamdi 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 introduce the notion of generalized weaker -contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.