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

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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.

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Authors and Affiliations

  1. Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan

    Chih-Sheng Chuang & Lai-Jiu Lin

  2. Department of Mathematics, National Chang kung University, Tainan, 701, Taiwan

    Chih-Sheng Chuang

Authors
  1. Chih-Sheng Chuang
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  2. Lai-Jiu Lin
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Correspondence to Lai-Jiu Lin.

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The authors wish to express their gratitude to the reviewers’s valuable suggestions and help.

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Chuang, CS., Lin, LJ. New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces. J Glob Optim 57, 533–547 (2013). https://doi.org/10.1007/s10898-012-0004-3

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  • DOI: https://doi.org/10.1007/s10898-012-0004-3

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