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Existence of Solutions to General Quasiequilibrium Problems and Applications

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Abstract

A general quasiequilibrium problem is proposed including, among others, equilibrium problems, implicit variational inequalities, and quasivariational inequalities involving multifunctions. Sufficient conditions for the existence of solutions with and without relaxed pseudomonotonicity are established. Even semicontinuity may not be imposed. These conditions improve several recent results in the literature.

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology of Vietnam, Hochiminh City, Vietnam

    N. X. Hai

  2. Department of Mathematics, International University at Hochiminh City, Hochimin City, Vietnam

    P. Q. Khanh

Authors
  1. N. X. Hai
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  2. P. Q. Khanh
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Corresponding author

Correspondence to P. Q. Khanh.

Additional information

Communicated by S. Schaible.

This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. The authors are very grateful to Professor Schaible and the referees for their valuable remarks and suggestions which helped to improve remarkably the paper.

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Hai, N.X., Khanh, P.Q. Existence of Solutions to General Quasiequilibrium Problems and Applications. J Optim Theory Appl 133, 317–327 (2007). https://doi.org/10.1007/s10957-007-9170-8

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  • DOI: https://doi.org/10.1007/s10957-007-9170-8

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