Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces

被引:6
作者
Tsar'kov, I. G. [1 ,2 ]
机构
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow, Russia
[2] Moscow Ctr Fundamental & Appl Math, Moscow, Russia
基金
俄罗斯科学基金会;
关键词
selection of a set-valued mapping; Michael's selection theorem; fixed point; asymmetric space; Chebyshev centre; convex set; epsilon-selection; PROJECTION; CONVEXITY;
D O I
10.4213/im9331e
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The Michael selection theorem is extended to the case of set-alued mappings with not necessarily convex values. Classical approximation problems on cone-spaces with symmetric and asymmetric seminorms are considered. In particular, conditions for existence of continuous selections for convex subsets of asymmetric spaces are studied. The problem of existence of a Chebyshev centre for a bounded set is solved in a semilinear space consisting of bounded convex sets with Hausdorff semimetric.
引用
收藏
页码:835 / 851
页数:17
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