Geodesic
Topological degree theory in fuzzy metric spaces
Archivum mathematicum, Tome 55 (2019) no. 2, pp. 83-96 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved. As an application, a fixed point theorem in the given context is presented.
The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved. As an application, a fixed point theorem in the given context is presented.
DOI : 10.5817/AM2019-2-83
Classification : 47H05, 47H09, 47H10, 54H25
Keywords: fuzzy metric space; $t$-norm of $h$-type; topological degree theory 
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Rashid, M.H.M. Topological degree theory in fuzzy metric spaces. Archivum mathematicum, Tome 55 (2019) no. 2, pp. 83-96. doi: 10.5817/AM2019-2-83

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