Article

# Common fuzzy fixed point theorems in ordered metric spaces

Mathematical and Computer Modelling (Impact Factor: 2.02). 05/2011; 53(s 9–10):1737–1741. DOI: 10.1016/j.mcm.2010.12.050

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**ABSTRACT:**In recent times, coupled, tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions. Roldán et al. showed a unified version of these results for nonlinear mappings in any number of variables (which were not necessarily permuted or ordered) introducing the notion of multidimensional coincidence point. Very recently, Choudhury et al. proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of George and Veeramani. In this paper, using the idea of coincidence point for nonlinear mappings in any number of variables, we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with Hadžić type t-norms. Then, we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied.Fuzzy Sets and Systems 09/2014; 251:71–82. · 1.88 Impact Factor -
##### Article: Some common fixed point theorems of multivalued mappings and fuzzy mappings in ordered metric spaces

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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.International Journal of Pure and Applied Mathematics. 01/2012; 75(2). - [Show abstract] [Hide abstract]

**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)).Abstract and Applied Analysis 01/2013; 2013. · 1.27 Impact Factor

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