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New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces

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  • Chih-Sheng Chuang
  • Lai-Jiu Lin

Abstract

Motivated by the Suzuki’s type fixed point theorems, we give several new existence theorems for scalar quasi-equilibrium problems, and vector quasi-equilibrium problem on complete metric spaces. We give important examples for our results. Note that the solution of quasi-equilibrium problem (resp. vector quasi-equilibrium problem) is unique under suitable conditions, and we can find the unique solution by the Picard iteration. Besides, we also give a new coincidence theorem on complete metric spaces. Finally, we give a new minimax theorem on complete metric spaces. Note that the solution of minimax theorem is unique under suitable conditions, and we can find the unique solution by the Picard iteration. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Chih-Sheng Chuang & Lai-Jiu Lin, 2013. "New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces," Journal of Global Optimization, Springer, vol. 57(2), pages 533-547, October.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:533-547
    DOI: 10.1007/s10898-012-0004-3
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    References listed on IDEAS

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    1. 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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