Compactness and the fixed point property in ℓ₁

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• 作者：T. Domí ; nguez-Benavides ^{tomasd@us.es" class="auth_mail" title="E-mail the corresponding author} ; M. Japó ; n ; ^{japon@us.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonexpansive mappings ; Uniformly Lipschitzian mappings ; Cascading nonexpansive mappings ; Fixed point ; Compact domain
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：444
• 期：1
• 页码：69-79
• 全文大小：356 K

文摘

In this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space ℓ₁${\ell }_1$. Nominally, our result involves nonexpansive mappings, uniformly Lipschitzian mappings and cascading nonexpansive mappings. We also extend the results to some more general classes of Banach spaces.