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关于“Fixed Points in Fuzzy Metric Spaces”一文的注记

01 Jan 1994-Vol. 14, Iss: 3, pp 473-474
About: The article was published on 1994-01-01 and is currently open access. It has received 176 citations till now.
Citations
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Journal ArticleDOI
TL;DR: A method for constructing a Hausdorff fuzzy metric on the set of the nonempty compact subsets of a given fuzzy metric space (in the sense of George and Veeramani) is proposed.

244 citations


Cites background from "关于“Fixed Points in Fuzzy Metric Spa..."

  • ...A simple but useful fact is that M (x; y; ) is nondecreasing for all x; y∈X [8]....

    [...]

Journal ArticleDOI
TL;DR: A Banach contraction theorem in M-complete non-Archimedean fuzzy metric spaces (under arbitrary t-norms) is proved and partially answering a question of Gregori and Sapena.

159 citations


Cites background from "关于“Fixed Points in Fuzzy Metric Spa..."

  • ...Grabiec [2] initiated the study of fixed point theory in fuzzy metric spaces, which is parallel to fixed point theory in probabilistic metric spaces (see [3,5])....

    [...]

Journal ArticleDOI
TL;DR: Some results on fuzzy contractive mappings in [V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002) 245-253] are extended to Edelstein fuzzy contractively mappings by modifying the notion of convergence in fuzzy metrics spaces.

128 citations


Cites background from "关于“Fixed Points in Fuzzy Metric Spa..."

  • ...The next continuity lemma can be found in [4] (also see [5, Theorem 12....

    [...]

Journal ArticleDOI
TL;DR: It is proved that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion and that for each fuzzy metrics space there is an ( up to uniform isomorphism) unique complete fuzzy metricspace that contains a dense subspace uniformly isomorphic to it.

127 citations


Cites background from "关于“Fixed Points in Fuzzy Metric Spa..."

  • ...A simple but useful fact [5] is that for each x; y∈X , the function M (x; y; ) is increasing....

    [...]

Journal Article
TL;DR: In this article, the authors present some common fixed point theorems for occasionally weakly compatible mappings in fuzzy metric spaces, which is a special case of fuzzy metric space.
Abstract: : This paper presents some common fixed point theorems for occasionally weakly compatible mappings in fuzzy metric spaces. Keywords : Occasionally weakly compatible mappings,fuzzy metric space.

108 citations


Cites background from "关于“Fixed Points in Fuzzy Metric Spa..."

  • ...…= 1 n whenever {xn} is a sequence in X such that lim fxn = lim g xn = x for some x in X. n n Definition 1.7 [5]: Two self maps f and g of a fuzzy metric space (X,M, *) are called reciprocally continuous on X if lim fgxn = fx and lim gfxn = gx n n whenever {xn} is a sequence in X such that lim fxn…...

    [...]

References
More filters
Journal ArticleDOI
TL;DR: A method for constructing a Hausdorff fuzzy metric on the set of the nonempty compact subsets of a given fuzzy metric space (in the sense of George and Veeramani) is proposed.

244 citations

Journal ArticleDOI
TL;DR: A Banach contraction theorem in M-complete non-Archimedean fuzzy metric spaces (under arbitrary t-norms) is proved and partially answering a question of Gregori and Sapena.

159 citations

Journal ArticleDOI
TL;DR: It is proved that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion and that for each fuzzy metrics space there is an ( up to uniform isomorphism) unique complete fuzzy metricspace that contains a dense subspace uniformly isomorphic to it.

127 citations

Journal Article
TL;DR: In this article, the authors present some common fixed point theorems for occasionally weakly compatible mappings in fuzzy metric spaces, which is a special case of fuzzy metric space.
Abstract: : This paper presents some common fixed point theorems for occasionally weakly compatible mappings in fuzzy metric spaces. Keywords : Occasionally weakly compatible mappings,fuzzy metric space.

108 citations

Journal Article
TL;DR: In this paper, some common fixed point theorems in complete fuzzy metric spaces are proved which generalize earlier results due to Vasuki (18), Chugh and Kumar (3) and others.
Abstract: Some common fixed point theorems in complete fuzzy metric spaces (in sense of Song (17) and Vasuki-Veeramani (19)) are proved which generalize earlier results due to Vasuki (18), Chugh and Kumar (3) and others. We also introduce the concept of R-weak com- mutativity of type (P ) in fuzzy metric spaces. Some related results and illustrative examples are also discussed.

81 citations