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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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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.

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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 Cheng Kung University, 701, Tainan, Taiwan

    Chih-Sheng Chuang

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  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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Chuang, CS., Lin, LJ. Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications. J Glob Optim 57, 829–841 (2013). https://doi.org/10.1007/s10898-012-9976-2

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  • DOI: https://doi.org/10.1007/s10898-012-9976-2

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