Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property ()

Sunny Chauhan, Wutiphol Sintunavarat, Poom Kumam

Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand.

R. H. Government Postgraduate College, Kashipur, India.

**DOI: **10.4236/am.2012.39145
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Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand.

R. H. Government Postgraduate College, Kashipur, India.

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

Keywords

Fuzzy Metric Space; Weakly Compatible Mappings; (E.A) Property; (CLR) Property; (JCLR) Property

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S. Chauhan, W. Sintunavarat and P. Kumam, "Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property," *Applied Mathematics*, Vol. 3 No. 9, 2012, pp. 976-982. doi: 10.4236/am.2012.39145.

Conflicts of Interest

The authors declare no conflicts of interest.

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