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Contraction, Lebesgue and Common Fixed Point Property of Fuzzy Metric Spaces
International Journal of Discrete Mathematics
Volume 5, Issue 2, December 2020, Pages: 10-14
Received: Aug. 18, 2020; Accepted: Oct. 12, 2020; Published: Oct. 30, 2020
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Gauri Shanker Sao, Department of Mathematics, Government Edpuganti Raghavendra Rao Post Graduate Science College, Atal Bihari Vajpayee Vishwavidyalaya University, Bilaspur, India
Swati Verma, Department of Mathematics, Omprakash Prakash Jindal University, Raigarh, India
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In this paper, we using contraction and contraction functions in complete fuzzy metric space and establish sequential characterization properties of Lebesgue fuzzy metric space and common fixed on it. Then first introduce a new type of Lebesgue fuzzy metric space, which is generalization of fuzzy metric space, second we study the topological properties of Lebesgue fuzzy metric space, third a relation between Lebesgue and weak G-complete, compact fuzzy metrics and Lebesgue integral mappings finally established characterization properties on it. We prove the existence of common fixed point and contraction mapping in fuzzy metric space using the property of Lebesgue fuzzy metric space and integral type of mappings. On the basis of these properties we are getting common fixed point of two mappings, three mappings and four mappings in a easy way as compared to old method like Banach contraction fixed point. Also coincidence fixed point theorem for two mapping, three mappings and four mappings using Lebesgue fuzzy metric space and integral type of mappings. Also contraction mappings property in fuzzy metric space is helpful to determine common fixed point in Lebesgue fuzzy metric space. We also discuss the Lebesgue property of several well-known fuzzy metric spaces in this paper and conclude uniqueness of common fixed point.
Fuzzy Metric Space, Completeness, Continuity, Contraction Function, Fixed Point, Lebesgue Property, G-complete
To cite this article
Gauri Shanker Sao, Swati Verma, Contraction, Lebesgue and Common Fixed Point Property of Fuzzy Metric Spaces, International Journal of Discrete Mathematics. Vol. 5, No. 2, 2020, pp. 10-14. doi: 10.11648/j.dmath.20200502.11
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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