Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON EQUILIBRIUM PROBLEMS WITHOUT CLOSURE OF THE CONSTRAINT SET AND APPLICATION TO MINIMAX PROBLEMS

  • Bui The Hung (Department of Mathematics Thai Nguyen University of Education) ;
  • Vilayvong Silikone (Department of Physics and Mathematics Teacher Pakse Teacher Training College)
  • Received : 2024.11.04
  • Accepted : 2025.03.21
  • Published : 2025.10.31
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Abstract

In this paper, we establish sufficient conditions for the existence of solutions to the set-valued equilibrium problem without requiring the closure of the constraint set. Additionally, the conditions for the semicontinuity and convexity of the objective function are only needed on a special subset of the constraint set, rather than covering its entire domain. As applications, we derive existence results for minimax problems on dense sets.

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References

  1. B. Alleche and V. D. Rădulescu, Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory, Nonlinear Anal. Real World Appl. 28 (2016), 251–268. https://doi.org/10.1016/j.nonrwa.2015.10.002
  2. X. Ding and K.-K. Tan, A minimax inequality with applications to existence of equilibrium point and fixed point theorems, Colloq. Math. 63 (1992), no. 2, 233–247. https://doi.org/10.4064/cm-63-2-233-247
  3. S. László and A. Viorel, Densely defined equilibrium problems, J. Optim. Theory Appl. 166 (2015), no. 1, 52-75. https://doi.org/10.1007/s10957-014-0702-8