Near Fixed Point Theorems in the Space of Fuzzy Numbers
The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-06-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/6/7/108 |
| _version_ | 1831838955359698944 |
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| author | Hsien-Chung Wu |
| author_facet | Hsien-Chung Wu |
| author_sort | Hsien-Chung Wu |
| collection | DOAJ |
| description | The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed structure can be defined on this space. This also says that the fixed point theorems established in the normed space cannot apply directly to the space of fuzzy numbers. The purpose of this paper is to propose the concept of near fixed point in the space of fuzzy numbers and to study its existence. In order to consider the contraction of fuzzy-number-valued function, the concepts of near metric space and near normed space of fuzzy numbers are proposed based on the almost identical concept. The concepts of Cauchy sequences in near metric space and near normed space of fuzzy numbers are also proposed. Under these settings, the existence of near fixed points of fuzzy-number-valued contraction function in complete near metric space and near Banach space of fuzzy numbers are established. |
| first_indexed | 2024-12-23T05:42:40Z |
| format | Article |
| id | doaj.art-9c21db1e80fc4a9b9e7e2bb633b18064 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-23T05:42:40Z |
| publishDate | 2018-06-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-9c21db1e80fc4a9b9e7e2bb633b180642022-12-21T17:58:08ZengMDPI AGMathematics2227-73902018-06-016710810.3390/math6070108math6070108Near Fixed Point Theorems in the Space of Fuzzy NumbersHsien-Chung Wu0Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, TaiwanThe fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed structure can be defined on this space. This also says that the fixed point theorems established in the normed space cannot apply directly to the space of fuzzy numbers. The purpose of this paper is to propose the concept of near fixed point in the space of fuzzy numbers and to study its existence. In order to consider the contraction of fuzzy-number-valued function, the concepts of near metric space and near normed space of fuzzy numbers are proposed based on the almost identical concept. The concepts of Cauchy sequences in near metric space and near normed space of fuzzy numbers are also proposed. Under these settings, the existence of near fixed points of fuzzy-number-valued contraction function in complete near metric space and near Banach space of fuzzy numbers are established.http://www.mdpi.com/2227-7390/6/7/108Cauchy sequencenear fixed pointnear metric space of fuzzy numbersnear normed space of fuzzy numbersnull set |
| spellingShingle | Hsien-Chung Wu Near Fixed Point Theorems in the Space of Fuzzy Numbers Mathematics Cauchy sequence near fixed point near metric space of fuzzy numbers near normed space of fuzzy numbers null set |
| title | Near Fixed Point Theorems in the Space of Fuzzy Numbers |
| title_full | Near Fixed Point Theorems in the Space of Fuzzy Numbers |
| title_fullStr | Near Fixed Point Theorems in the Space of Fuzzy Numbers |
| title_full_unstemmed | Near Fixed Point Theorems in the Space of Fuzzy Numbers |
| title_short | Near Fixed Point Theorems in the Space of Fuzzy Numbers |
| title_sort | near fixed point theorems in the space of fuzzy numbers |
| topic | Cauchy sequence near fixed point near metric space of fuzzy numbers near normed space of fuzzy numbers null set |
| url | http://www.mdpi.com/2227-7390/6/7/108 |
| work_keys_str_mv | AT hsienchungwu nearfixedpointtheoremsinthespaceoffuzzynumbers |