Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications

Chih-Sheng Chuang () and Lai-Jiu Lin ()

Journal of Global Optimization, 2013, vol. 57, issue 3, 829-841

Abstract: In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some mapping. We also show that this unique solution can be obtained by Picard’s iteration method. We also get new minimax theorem, and existence theorems for common solution of fixed point and optimization problem on complete metric spaces. Our results are different from any existence theorems for quasi-equilibrium problems and minimax theorems in the literatures. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Equilibrium problem; Fixed point; Minimax theorem; Nonlinear mappings; Banach limit; Mean (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9976-2

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