On the splitting problem for selections

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:355

Article

Balashov, Maxim V.²  Repovs, Dusan^1,3 

[1] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

[2] Moscow Inst Phys & Technol, Dept Higher Math, Dolgoprudnyi 141700, Moscow Region, Russia

[3] Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia

关键词: Approximate splitting problem;    Set-valued mapping;    Continuous selection;    Lipschitz selection;    P-set;    Finite-dimensional Banach space;    Hilbert space;    Hausdorff metric;    Minkowski-Pontryagin difference;    Geometric difference;    Chebyshev center;    Steiner point;   

DOI  :  10.1016/j.jmaa.2009.01.051

来源: Elsevier

【 摘 要 】

We investigate when does the Repovs-Semenov splitting problem for selections have an affirmative solution for continuous set-valued mappings in finite-dimensional Banach spaces. We prove that this happens when images of set-valued mappings or even their graphs are P-sets (in the sense of Balashov) or strictly convex sets. We also consider an example which shows that there is no affirmative solution of this problem even in the simplest case in R-3. We also obtain affirmative solution of the approximate splitting problem for Lipschitz continuous selections in the Hilbert space. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free