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Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems

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Abstract

Applying generalized KKM-type theorems established in our previous paper (Khanh et al. in Nonlinear Anal. 71:1227–1234, 2009), we prove the existence of solutions to a general variational inclusion problem, which contains most of the existing results of this type. As applications, we obtain minimax theorems in various settings and saddle-point theorems in particular. Examples are given to explain advantages of our results.

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Authors and Affiliations

  1. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    P. Q. Khanh

  2. Department of Mathematics, Information Technology College of Hochiminh City, Hoa Thanh, Tan Phu, Hochiminh City, Vietnam

    N. H. Quan

Authors
  1. P. Q. Khanh
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  2. N. H. Quan
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Correspondence to P. Q. Khanh.

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Communicated by P.L. Yu.

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Khanh, P.Q., Quan, N.H. Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems. J Optim Theory Appl 146, 640–653 (2010). https://doi.org/10.1007/s10957-010-9690-5

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  • DOI: https://doi.org/10.1007/s10957-010-9690-5

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