About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions

被引：0

作者：

Lam Quoc Anh

Phan Quoc Khanh

Dinh Ngoc Quy

机构：

[1] Cantho University,Department of Mathematics

[2] Vietnam National University Hochiminh City,Department of Mathematics, International University

来源：

Set-Valued and Variational Analysis | 2014年 / 22卷

关键词：

Semi-limits; Semicontinuity; Solution maps; Quasivariational inclusions; Quasivariational relation problems; Quasivariational equilibrium problems; 90C31; 49J53;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature.

引用

页码：533 / 555

页数：22

共 50 条

[21] Topological Stability and Entropy for Certain Set-valued Maps
Yu Zhang
Yu Jun Zhu
[J]. Acta Mathematica Sinica, English Series, 2024, 40 : 962 - 984
[22] Approximation of continuous set-valued maps by constant set-valued maps with image balls
S. I. Dudov
A. B. Konoplev
[J]. Mathematical Notes, 2007, 82 : 469 - 473
[23] Approximation of continuous set-valued maps by constant set-valued maps with image balls
Dudov, S. I.
Konoplev, A. B.
[J]. MATHEMATICAL NOTES, 2007, 82 (3-4) : 469 - 473
[24] FIXED POINTS OF SOFT SET-VALUED MAPS WITH APPLICATIONS TO DIFFERENTIAL INCLUSIONS
Shagari, Mohammed Shehu
Azam, Akbar
[J]. SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, 2020, 38 (04): : 2083 - 2107
[25] ON SELECTIONS OF SET-VALUED MAPS SATISFYING SOME INCLUSIONS IN A SINGLE VARIABLE
Piszczek, Magdalena
[J]. MATHEMATICA SLOVACA, 2015, 65 (06) : 1445 - 1456
[26] ON SINGLE-VALUEDNESS OF SET-VALUED MAPS SATISFYING LINEAR INCLUSIONS
Nikodem, Kazimierz
Popa, Dorian
[J]. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2009, 3 (01): : 44 - 51
[27] A CALCULUS FOR SET-VALUED MAPS AND SET-VALUED EVOLUTION-EQUATIONS
ARTSTEIN, Z
[J]. SET-VALUED ANALYSIS, 1995, 3 (03): : 213 - 261
[28] Set-valued stable maps
Ostrovsky, AV
[J]. TOPOLOGY AND ITS APPLICATIONS, 2000, 104 (1-3) : 227 - 236
[29] On subdifferentials of set-valued maps
Baier, J
Jahn, J
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1999, 100 (01) : 233 - 240
[30] On Subdifferentials of Set-Valued Maps
J. Baier
J. Jahn
[J]. Journal of Optimization Theory and Applications, 1999, 100 : 233 - 240

← 1 2 3 4 5 →