Berge's maximum theorem to vector-valued functions with some applications
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Authors
Qiu Xiaoling
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China.
Peng Dingtao
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China.
Yu Jian
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China.
Abstract
In this paper, we introduce pseudocontinuity for Berge’s maximum theorem for vector-valued functions which is weaker
than semicontinuity. We prove the Berge’s maximum theorem for vector-valued functions with pseudocontinuity and obtain the
set-valued mapping of the solutions is upper semicontinuous with nonempty and compact values. As applications, we derive
some existence results for weakly Pareto-Nash equilibrium for multiobjective games and generalized multiobjective games both
with pseudocontinuous vector-valued payoffs. Moreover, we obtain the existence of essential components of the set of weakly
Pareto-Nash equilibrium for these discontinuous games in the uniform topological space of best-reply correspondences. Some
examples are given to investigate our results.
Share and Cite
ISRP Style
Qiu Xiaoling, Peng Dingtao, Yu Jian, Berge's maximum theorem to vector-valued functions with some applications, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1861--1872
AMA Style
Xiaoling Qiu, Dingtao Peng, Jian Yu, Berge's maximum theorem to vector-valued functions with some applications. J. Nonlinear Sci. Appl. (2017); 10(4):1861--1872
Chicago/Turabian Style
Xiaoling, Qiu, Dingtao, Peng, Jian, Yu. "Berge's maximum theorem to vector-valued functions with some applications." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1861--1872
Keywords
- Maximum theorem
- vector-valued functions
- set-valued mapping
- pseudocontinuity
- weakly Pareto-Nash equilibrium
- essential components.
MSC
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