Common fuzzy fixed point theorems in ordered metric spaces

Mathematical and Computer Modelling (Impact Factor: 1.41). 05/2011; 53(s 9–10):1737–1741. DOI: 10.1016/j.mcm.2010.12.050
Source: DBLP


We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contractive condition in complete ordered spaces. Our results provide extension as well as substantial improvements of several well-known results in the existing literature and initiate the study of fuzzy fixed point theorems in ordered spaces.

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Available from: Bosko Damjanovic, Jul 05, 2014
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    • "(see, e.g., [23] [24]). Let (í µí±‹, í µí±‘) and (í µí±‹, í µí±) be a metric space and a partial metric space, respectively. "
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    ABSTRACT: We study the existence and uniqueness of coincidence point for nonlinear mappings of any number of arguments under a weak (ψ, φ)-contractivity condition in partial metric spaces. The results we obtain generalize, extend, and unify several classical and very recent related results in the literature in metric spaces (see Aydi et al. (2011), Berinde and Borcut (2011), Gnana Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapınar and Luong (2012), Lakshmikantham and Ćirić (2009), Luong and Thuan (2011), and Roldán et al. (2012)) and in partial metric spaces (see Shatanawi et al. (2012)).
    Full-text · Article · Jul 2013 · Abstract and Applied Analysis
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    • "Ran and Reurings [17] first investigated the existence of fixed points in a partially ordered metric spaces and they were followed by Nieto and Lopez [16], Hajrani and Sadarangani [8], Kadelberg et al [11] (in a ordered cone metric space),etc. Also recently L. Ciric et al [7] have considered fuzzy common fixed theorems in ordered metric spaces and we can modify the last part of their proof following the proof of Theorem 55 of Bose and Roychowdhury [4] where we proved two fixed point theorems concerning a pair of fuzzy weakly (generalized) contractive mappings. We shall consider the ordered metric space version of these in another paper. "
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    ABSTRACT: Heilpern [9] introduced the concept of fuzzy mappings and proved a fixed point theorem for fuzzy contraction mappings. Generalizing Heilpern’s result, Bose and Sahani [5] proved a common fixed point theorem for a pair of generalized fuzzy contraction mappings and also a fixed point theorem for nonexpansive fuzzy mappings. Since then, many authors have generalized Bose and Sahani’s results in different directions. Also Bose and mukherjee (see [2], [3]) considered common fixed points of a pair of multivalued mappings and a sequence of single valued mappings. We present several theorems which are generalized to ordered metric space setting.In Section 3, we present our remarks concerning some generalizations of the main theorm of Bose and Sahani.Three such results, of Vijayaraju and Marudai [18], Azam and Arshad [1], and B.S. Lee et al [13] are discussed and a correct proof of the main theorem of Vijayaraju and Marudai has ben presented using a tecnique of Bose and Mukherjee [2]. In Section 4, we present several new theorems in ordered metric space setting. One is a version of the fixed point theorem for a pair of multivalued mappings of Bose and Mukherjee in ordered metric space setting and the other is a new version of the main theorem of Bose and Sahani in orderd metric space setting. Also we present a few results concerning common fixed point of a sequence of such mappings in ordered metric space setting.
    Full-text · Article · Jan 2012 · International Journal of Pure and Applied Mathematics
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    ABSTRACT: We prove a common fixed point theorem for mappings under ϕ-contractive conditions in fuzzy metric spaces. We also give an example to illustrate the theorem. The result is a genuine generalization of the corresponding result of S. Sedghi et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3-4, A, 1298–1304 (2010; Zbl 1180.54060)].
    Preview · Article · Jan 2011 · Fixed Point Theory and Applications
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