The rise and fall of L-spaces, II
In 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder fixed point theorem to multimaps on non-compact co...
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| Format: | Article |
| Language: | English |
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ATNAA
2021-01-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1471486 |
| _version_ | 1797909622808379392 |
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| author | Sehie Park |
| author_facet | Sehie Park |
| author_sort | Sehie Park |
| collection | DOAJ |
| description | In 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder fixed point theorem to multimaps on non-compact convex sets. Since then several groups of the L-space theorists introduced coercivity families and applied them to L-spaces,
H-spaces, etc. In this article, we show that better forms of such works can be deduced from a general KKM theorem on abstract convex spaces in our previous works. Consequently, all of known KKM theoretic results on L-spaces related coercivity families are extended to corresponding better forms on abstract convex spaces.
This article is a continuation of our [38] and a revised and extended version of [34]. |
| first_indexed | 2024-04-10T11:12:32Z |
| format | Article |
| id | doaj.art-801f4fef41cb4388be124c977c5d4daa |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T11:12:32Z |
| publishDate | 2021-01-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-801f4fef41cb4388be124c977c5d4daa2023-02-15T16:19:02ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482021-01-015172410.31197/atnaa.847835The rise and fall of L-spaces, IISehie ParkIn 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder fixed point theorem to multimaps on non-compact convex sets. Since then several groups of the L-space theorists introduced coercivity families and applied them to L-spaces, H-spaces, etc. In this article, we show that better forms of such works can be deduced from a general KKM theorem on abstract convex spaces in our previous works. Consequently, all of known KKM theoretic results on L-spaces related coercivity families are extended to corresponding better forms on abstract convex spaces. This article is a continuation of our [38] and a revised and extended version of [34].https://dergipark.org.tr/tr/download/article-file/1471486kkm theoremfan's 1961 kkm lemma1984 kkm theoremminimax inequalityabstract convex space(partial) kkm spacefan-browder fiixed point theorem |
| spellingShingle | Sehie Park The rise and fall of L-spaces, II Advances in the Theory of Nonlinear Analysis and its Applications kkm theorem fan's 1961 kkm lemma 1984 kkm theorem minimax inequality abstract convex space (partial) kkm space fan-browder fiixed point theorem |
| title | The rise and fall of L-spaces, II |
| title_full | The rise and fall of L-spaces, II |
| title_fullStr | The rise and fall of L-spaces, II |
| title_full_unstemmed | The rise and fall of L-spaces, II |
| title_short | The rise and fall of L-spaces, II |
| title_sort | rise and fall of l spaces ii |
| topic | kkm theorem fan's 1961 kkm lemma 1984 kkm theorem minimax inequality abstract convex space (partial) kkm space fan-browder fiixed point theorem |
| url | https://dergipark.org.tr/tr/download/article-file/1471486 |
| work_keys_str_mv | AT sehiepark theriseandfalloflspacesii AT sehiepark riseandfalloflspacesii |