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Abstract and Applied Analysis
Volume 2013, Article ID 278340, 10 pages
Research Article

Common Fixed Point for Self-Mappings Satisfying an Implicit Lipschitz-Type Condition in Kaleva-Seikkala's Type Fuzzy Metric Spaces

Mathematics and Information Technology School, Jiangsu Second Normal University, Nanjing 210013, China

Received 18 September 2013; Accepted 19 November 2013

Academic Editor: Jesús García Falset

Copyright © 2013 Ming-Liang Song and Xiu-Juan Zhu. 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.


We first introduce the new real function class satisfying an implicit Lipschitz-type condition. Then, by using -type real functions, some common fixed point theorems for a pair of self-mappings satisfying an implicit Lipschitz-type condition in fuzzy metric spaces (in the sense of Kaleva and Seikkala) are established. As applications, we obtain the corresponding common fixed point theorems in metric spaces. Also, some examples are given, which show that there exist mappings which satisfy the conditions in this paper but cannot satisfy the general contractive type conditions.