Endpoints of multivalued nonexpansive mappings in geodesic spaces

Fixexd point theory and applications

Bancha Panyanak¹ 

[1] Department of Mathematics, Faculty of Science, Chaing Mai University, Chiang Mai, Thailand

关键词: endpoint;    fixed point;    multivalued nonexpansive mapping;    Banach space;    CAT(0) space;   

DOI  :  10.1186/s13663-015-0398-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if and only if it has the approximate endpoint property. This is the first result regarding the existence of endpoints for such kind of mappings even in Hilbert spaces. The related result in a complete CAT(0) space is also given.

【 授权许可】

CC BY