Abstract and Applied Analysis

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

Abstract

We first introduce the new real function class $ℱ$ satisfying an implicit Lipschitz-type condition. Then, by using $ℱ$-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.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 278340, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512209

Digital Object Identifier
doi:10.1155/2013/278340

Mathematical Reviews number (MathSciNet)
MR3143556

Zentralblatt MATH identifier
1294.54042

Citation

Song, Ming-Liang; Zhu, Xiu-Juan. Common Fixed Point for Self-Mappings Satisfying an Implicit Lipschitz-Type Condition in Kaleva-Seikkala's Type Fuzzy Metric Spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 278340, 10 pages. doi:10.1155/2013/278340. https://projecteuclid.org/euclid.aaa/1393512209

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