Journal Article•
Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces
TL;DR: In this article, a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg) property is presented. But this theorem is not applicable to the case of pairwise commuting.
Abstract: The aim of this paper is to prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg) property. An example is also furnished which demonstrates the validity of our main result. As an application to our main result, we present a fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting. Our results improve the results of Sedghi, Shobe and Aliouche [A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces, Gen. Math. 18(3) (2010), 3-12 MR2735558].
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03 Jun 2013
TL;DR: In this paper, the authors proved some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces.
Abstract: We prove some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces. The proved results generalize and extend some of the known results in the literature.
35 citations
Journal Article•
23 citations
TL;DR: In this paper, the authors present a survey that provides a brief historical account of the development through definitions and comparison of weaker forms of commuting mappings set brought together from some applications oriented point of view.
Abstract: This paper presents a survey that aims to provide a brief historical account of the development through the definitions and comparison of weaker forms of commuting mappings set brought together from some applications oriented point of view.
22 citations
TL;DR: In this paper, Rao et al. utilized the notion of common limit range property to prove unified fixed point theorems for weakly compatible mappings in fuzzy metric spaces satisfying an implicit relation.
Abstract: The object of this paper is to utilize the notion of common limit range property to prove unified fixed point theorems for weakly compatible mappings in fuzzy metric spaces satisfying an implicit relation due to Rao et al. (Hacet. J. Math. Stat. 37(2):97-106, 2008). Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. As an application to our main result, we prove an integral type fixed point theorem in fuzzy metric space.
17 citations
References
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Book•
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01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
52,705 citations
Journal Article•
TL;DR: The aim of this paper is to apply the concept of fuzziness to the clasical notions of metric and metric spaces and to compare the obtained notions with those resulting from some other, namely probabilistic statistical, generalizations of metric spaces.
Abstract: The adjective "fuzzy" seems to be a very popular and very frequent one in the contemporary studies concerning the logical and set-theoretical foundations of mathematics. The main reason of this quick development is, in our opinion, easy to be understood. The surrounding us world is full of uncertainty, the information we obtain from the environment, the notions we use and the data resulting from our observation or measurement are, in general, vague and incorrect. So every formal description of the real world or some of its aspects is, in every case, only an approxima tion and an idealization of the actual state. The notions like fuzzy sets, fuzzy orderings, fuzzy languages etc. enable to handle and to study the degree of uncertainty mentioned above in a purely mathematic and formal way. A very brief survey of the most interest ing results and applications concerning the notion of fuzzy set and the related ones can be found in [l]. The aim of this paper is to apply the concept of fuzziness to the clasical notions of metric and metric spaces and to compare the obtained notions with those resulting from some other, namely probabilistic statistical, generalizations of metric spaces. Our aim is to write this paper on a quite self-explanatory level the references being necessary only for the reader wanting to study these matters in more details.
1,438 citations
TL;DR: In this paper, a Hausdorff topology on a fuzzy metric space was defined, and Baire's theorem for fuzzy metric spaces was proved for the first time in the fuzzy metric domain.
1,325 citations
TL;DR: In this paper, the well-known fixed point theorems of Banach and Edelstein are extended to fuzzy metric spaces in the settle of Kramosil and Michalek.
824 citations