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The Essential Component of the Solution Set for Vector Equilibrium Problems

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Abstract

In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector equilibrium problem satisfying some conditions.

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References

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Authors and Affiliations

  1. Department of Mathematics, Zhaoqing University, Zhaoqing, 526061, Guangdong, P. R. China

    Qun Luo

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  1. Qun Luo
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Correspondence to Qun Luo.

Additional information

Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China.

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Luo, Q. The Essential Component of the Solution Set for Vector Equilibrium Problems. J Glob Optim 34, 589–595 (2006). https://doi.org/10.1007/s10898-005-1648-z

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  • DOI: https://doi.org/10.1007/s10898-005-1648-z

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