An approximation theorem and generic convergence for equilibrium problems

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by th...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2018; no. 1; pp. 30 - 12
Main Authors: Qiu, Xiaoling, Jia, Wensheng, Peng, Dingtao
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 2018
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Approximation theorem
Equilibrium problems
Generic convergence
Mathematics
Mathematics and Statistics
Pseudocontinuity
Set-valued mapping
Pseudocontinuity
Generic convergence
Approximation theorem
Equilibrium problems
Set-valued mapping
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1617-y