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On the Brézis Nirenberg Stampacchia-type theorems and their applications

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  • M. Fakhar
  • M. Lotfipour
  • J. Zafarani

Abstract

In this paper, we obtain several new generalized KKM-type theorems under a new coercivity condition and the condition of intersectionally closedness which improves condition of transfer closedness. As applications, we obtain new versions of equilibrium problem, minimax inequality, coincidence theorem, fixed point theorem and an existence theorem for an 1-person game. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • M. Fakhar & M. Lotfipour & J. Zafarani, 2013. "On the Brézis Nirenberg Stampacchia-type theorems and their applications," Journal of Global Optimization, Springer, vol. 55(4), pages 751-770, April.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:4:p:751-770
    DOI: 10.1007/s10898-012-9965-5
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    References listed on IDEAS

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    1. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    2. M. Fakhar & J. Zafarani, 2004. "Generalized Equilibrium Problems for Quasimonotone and Pseudomonotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 349-364, November.
    3. L. J. Lin & W. P. Wan, 2004. "KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 105-122, October.
    4. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    5. M. Fakhar & J. Zafarani, 2005. "Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions 1," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 109-124, July.
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