ON ONE-SIDED LIPSCHITZ STABILITY OF SET-VALUED CONTRACTIONS

被引：13
|
作者：
Adly, S. [1 ]
Dontchev, A. L. [2 ]
Thera, M. [1 ]
机构：
[1] Univ Limoges, Lab XLIM, F-87060 Limoges, France
[2] Math Reviews, Ann Arbor, MI USA
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2014年 / 35卷 / 7-9期
基金：
澳大利亚研究理事会; 美国国家科学基金会;
关键词：
Composition; Differential inclusions; Fixed points; Lyusternik-Graves theorem; Lipschitz stability; Set-valued mappings; FIXED-POINT STABILITY; COINCIDENCE POINTS; METRIC-SPACES; COVERING MAPPINGS; EQUATIONS; MAPS;
D O I：
10.1080/01630563.2014.895760
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give conditions under which the distance from a point x to the set of fixed points of the composition of the set-valued mappings F and G is bounded by a constant times the smallest distance between F-1(x) and G(x). This estimate allows us to significantly sharpen a result by T.-C. Lim [10] regarding fixed-points stability of set-valued contractions. A global version of the Lyusternik-Graves theorem is obtained from this estimate as well. We apply the generalization of Lim's result to establish one-sided Lipschitz properties of the solution mapping of a differential inclusion with a parameter.
引用
收藏
页码：837 / 850
页数：14
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