The demiclosedness principle for mean nonexpansive mappings

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• 作者：Torrey M. Gallagher ^{tmg34@pitt.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Demiclosed ; Mean nonexpansive ; Fixed point ; Approximate fixed point sequence ; Uniform convexity ; Opial's property
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：439
• 期：2
• 页码：832-842
• 全文大小：327 K

文摘

In this paper, we establish the demiclosedness principle for the class of mean nonexpansive mappings, introduced in 2007 by Goebel and Japón Pineda, defined on closed, convex subsets of Banach spaces satisfying Opial's condition. We also establish the demiclosedness principle for a subclass of the mean nonexpansive maps whose domains are closed, bounded, convex sets in uniformly convex spaces. These results extend known demiclosedness results for nonexpansive maps and lead to some fixed point results for mean nonexpansive maps which partially answer an open question posed by Goebel and Japón Pineda.