Topological degree theory in fuzzy metric spaces

M.H.M. Rashid

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 2, page 83-96
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Rashid, M.H.M.. "Topological degree theory in fuzzy metric spaces." Archivum Mathematicum 055.2 (2019): 83-96. <http://eudml.org/doc/294403>.

@article{Rashid2019,
abstract = {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.},
author = {Rashid, M.H.M.},
journal = {Archivum Mathematicum},
keywords = {fuzzy metric space; $t$-norm of $h$-type; topological degree theory},
language = {eng},
number = {2},
pages = {83-96},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Topological degree theory in fuzzy metric spaces},
url = {http://eudml.org/doc/294403},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Rashid, M.H.M.
TI - Topological degree theory in fuzzy metric spaces
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 2
SP - 83
EP - 96
AB - 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.
LA - eng
KW - fuzzy metric space; $t$-norm of $h$-type; topological degree theory
UR - http://eudml.org/doc/294403
ER -

References

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