Spherical nonspreadingness of resolvents of convex functions in geodesic spaces

被引：21
|
作者：
Kimura, Yasunori [1 ]
Kohsaka, Fumiaki [2 ]
机构：
[1] Toho Univ, Dept Informat Sci, Funabashi, Chiba 2748510, Japan
[2] Tokai Univ, Dept Math Sci, Hiratsuka, Kanagawa 2591292, Japan
来源：
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2016年 / 18卷 / 01期
关键词：
Convex function; fixed point; geodesic space; minimizer; resolvent; spherically nonspreading mapping; BANACH-SPACES; FIXED-POINTS; HARMONIC MAPS; METRIC-SPACES; CONVERGENCE; MAPPINGS; CURVATURE; OPERATORS; THEOREMS; SUBSETS;
D O I：
10.1007/s11784-015-0267-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose the concepts of a spherically nonspreading mapping and a firmly spherically nonspreading mapping in a complete geodesic space with curvature bounded above by one and we prove that the resolvent of a proper lower semicontinuous convex function in that space is both well defined and firmly spherically nonspreading. We further discuss the existence and approximation of fixed points of such mappings and apply our results to convex optimization in geodesic spaces.
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页码：93 / 115
页数：23
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