Fixed Points and Variational Principles with Applications to Capability Theory of Wellbeing via Variational Rationality
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- 作者：T. Q. Bao ; B. S. Mordukhovich ; A. Soubeyran
- 关键词：Variational analysis and optimization ; Variational principles ; Fixed point theory ; Capacity approach to wellbeing ; Variational rationality ; Primary 49J53 ; 49J52 ; Secondary 90C29 ; 90C30
- 刊名：Set-Valued and Variational Analysis
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：23
- 期：2
- 页码：375-398
- 全文大小：392 KB
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B. S. Mordukhovich (2)
A. Soubeyran (3)
1. Department of Mathematics & Computer Science, Northern Michigan University, Marquette, Michigan, 49855, USA
2. Department of Mathematics, Wayne State University, Detroit, Michigan, USA
3. Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS, Marseille, 13002, France - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Analysis
Geometry - 出版者：Springer Netherlands
- ISSN：1877-0541
文摘
In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational principle for set-valued mappings acting from quasimetric spaces to vector spaces with variable ordering structures, which can be treated as a far-going extension of Ekeland’s variational principle to this setting. Both of these results are motivated by applications to adaptive dynamical aspects of Sen’s capability theory of wellbeing. As consequence of our mathematical results, we develop new applications to such human behavioral models by using a recent variational rationality approach to behavioral sciences.