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Volume 12
Issue 14
10.3390/math12142165
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Fixed-Point Theorems for Fuzzy Mappings

by
Allan Edley Ramos de Andrade
1,* and
Vinícius Francisco Wasques
2
1
Federal University of Mato Grosso do Sul, CPTL, Três Lagoas 79613-000, Brazil
2
Ilum School of Science, CNPEM, Campinas 13087-548, Brazil
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(14), 2165; https://doi.org/10.3390/math12142165
Submission received: 4 June 2024 / Revised: 1 July 2024 / Accepted: 7 July 2024 / Published: 10 July 2024
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
Versions Notes

Abstract

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra.
Keywords: fuzzy topology; fuzzy sets; fuzzy mapping; fixed point; coincidence point; multi-valued map fuzzy topology; fuzzy sets; fuzzy mapping; fixed point; coincidence point; multi-valued map

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MDPI and ACS Style

Andrade, A.E.R.d.; Wasques, V.F. Fixed-Point Theorems for Fuzzy Mappings. Mathematics 2024, 12, 2165. https://doi.org/10.3390/math12142165

AMA Style

Andrade AERd, Wasques VF. Fixed-Point Theorems for Fuzzy Mappings. Mathematics. 2024; 12(14):2165. https://doi.org/10.3390/math12142165

Chicago/Turabian Style

Andrade, Allan Edley Ramos de, and Vinícius Francisco Wasques. 2024. "Fixed-Point Theorems for Fuzzy Mappings" Mathematics 12, no. 14: 2165. https://doi.org/10.3390/math12142165

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