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The Scientific World Journal
Volume 2014, Article ID 981578, 12 pages
Research Article

Implicit Contractive Mappings in Modular Metric and Fuzzy Metric Spaces

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

Received 21 April 2014; Accepted 26 May 2014; Published 5 June 2014

Academic Editor: Abdullah Alotaibi

Copyright © 2014 N. Hussain and P. Salimi. 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.


The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized -admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.