Journal of Applied Mathematics
Volume 2012 (2012), Article ID 890678, 18 pages
http://dx.doi.org/10.1155/2012/890678
Research Article

Common Fixed Point Theorems in a New Fuzzy Metric Space

Weiquan Zhang,1 Dong Qiu,2 Zhifeng Li,1 and Gangqiang Xiong1

1School of Information Engineering, Guangdong Medical College, Dongguan, Guangdong 523808, China
2College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, China

Received 26 October 2011; Accepted 1 December 2011

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Weiquan Zhang 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 generalize the Hausdorff fuzzy metric in the sense of Rodríguez-López and Romaguera, and we introduce a new 𝑀 ∞ -fuzzy metric, where 𝑀 ∞ -fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number. Moreover, under 𝜙 -contraction condition, in the fuzzy metric space, we give some common fixed point theorems for fuzzy mappings.