Publication Date:
2013-02-26
Description:
In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. In order to do that, we consider a slight modification of the concept of tripled fixed point introduced by Berinde et al. [V. Berinde, M. Borcut, \emph{Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces}, Nonlinear Anal. \textbf{74}(2011) 4889--4897] for nonlinear mappings. Additionally, we obtain some fixed point theorems for metric spaces. These results generalize, extend and unify several classical and very recent related results in literature. For instance, we obtain an extension of the Theorem 4.1 in [X-H. Zhu, J-Z. Xiao, \emph{Note on \textquotedblleft Coupled fixed point theorems for contractions in fuzzy metric spaces\textquotedblright}, Nonlinear Anal. \textbf{74}(2011) 5475-5479] and a version in non-partially ordered sets of the Theorem 2.2 in [T.G. Bhaskar, V. Lakshmikantham, \emph{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65}(2006) 1379--1393]. As application, we solve a kind of Lipschitzian systems in three variables and an integral system. Finally, examples to support our results are also given.
Print ISSN:
1687-1820
Electronic ISSN:
1687-1812
Topics:
Mathematics
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