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

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  • Chih-Sheng Chuang
  • Lai-Jiu Lin

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

Suggested Citation

  • Chih-Sheng Chuang & Lai-Jiu Lin, 2013. "Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications," Journal of Global Optimization, Springer, vol. 57(3), pages 829-841, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:829-841
    DOI: 10.1007/s10898-012-9976-2
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    References listed on IDEAS

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    1. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    2. Jia Chen & Yeol Cho & Jong Kim & Jun Li, 2011. "Multiobjective optimization problems with modified objective functions and cone constraints and applications," Journal of Global Optimization, Springer, vol. 49(1), pages 137-147, January.
    3. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
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