Contraction, Lebesgue and Common Fixed Point Property of Fuzzy Metric Spaces
Gauri Shanker Sao,
Swati Verma
Issue:
Volume 5, Issue 2, December 2020
Pages:
10-14
Received:
18 August 2020
Accepted:
12 October 2020
Published:
30 October 2020
Abstract: 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.
Abstract: 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 proper...
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