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Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems

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Abstract

In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    N. J. Huang

  2. Department of Mathematics, China West Normal University, Nanchong, Sichuan, People’s Republic of China

    J. Li

  3. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan

    J. C. Yao

Authors
  1. N. J. Huang
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  2. J. Li
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  3. J. C. Yao
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Corresponding author

Correspondence to J. C. Yao.

Additional information

Communicated by X.Q. Yang.

This work was supported by the National Natural Science Foundation of China, the Youth Foundation, Sichuan Education Department of China, the National Natural Science Foundation, Sichuan Education Department of China (2004C018), and a grant from the National Science Council of ROC.

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Huang, N.J., Li, J. & Yao, J.C. Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems. J Optim Theory Appl 133, 201–212 (2007). https://doi.org/10.1007/s10957-007-9202-4

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