Journal of Guangxi Normal University(Natural Science Edition) ›› 2023, Vol. 41 ›› Issue (2): 98-105.doi: 10.16088/j.issn.1001-6600.2022010701

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Connectedness of the Strong Efficient Solution Set for Vector Equilibrium Problems

YANG Xiufeng, FAN Jianghua*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2022-01-07 Revised:2022-02-28 Online:2023-03-25 Published:2023-04-25

Abstract: The connectedness of the strong efficient solution set for vector equilibrium problems in reflexive Banach spaces is studied in this paper. A new nonlinear function is established, and a non-convex non-closed set and a compact set can be separated by the new nonlinear function. It is shown that the solution set of the strong vector equilibrium problems equals to the union of the solution set of a series of non-linear scalar problems. The connectedness of the strong efficient solution set for vector equilibrium problems is obtained.

Key words: vector equilibrium problems, connectedness, nonconvex separation theorem, strong efficient solutions set

CLC Number: 

  • O224.1
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