Some fixed point theorems on non-convex sets
In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$
| 出版年: | Applied General Topology |
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| 主要な著者: | , , |
| フォーマット: | 論文 |
| 言語: | 英語 |
| 出版事項: |
Universitat Politècnica de València
2017-10-01
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| 主題: | |
| オンライン･アクセス: | https://polipapers.upv.es/index.php/AGT/article/view/7452 |
| 要約: | In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$ |
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| ISSN: | 1576-9402 1989-4147 |