The behavior of fixed point free nonexpansive mappings in geodesic spaces

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• 作者：Bozena Piatek ^{Bozena.Piatek@polsl.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Geodesic spaces ; Nonexpansive mappings ; Geodesic boundary ; Picard iterative sequence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：1071-1083
• 全文大小：367 K

文摘

Dropping the existence of fixed points of a nonexpansive mapping is an interesting and unusual task in metric fixed point theory. Hyperbolic geometry proved to be very relevant in the study of the behavior of fixed point free nonexpansive mappings. In this work we generalize some of the results in that direction in geodesic spaces. More precisely, we show under which additional assumptions the Picard iterative sequence of a mapping defined on a hyperbolic geodesic space tends to a point of the boundary.