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Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces

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  • Lu-Chuan Ceng
  • Jen-Chih Yao

Abstract

In this paper, utilizing the properties of the generalized f -projection operator and the well-known KKM and Kakutani–Fan–Glicksberg theorems, under quite mide assumptions, we derive some new existence theorems for the generalized set-valued mixed variational inequality and the generalized set-valued mixed quasi-variational inequality in reflexive and smooth Banach spaces, respectively. The results presented in this paper can be viewed as the supplement, improvement and extension of recent results in Wu and Huang (Nonlinear Anal 71:2481–2490, 2009 ). Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Lu-Chuan Ceng & Jen-Chih Yao, 2013. "Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces," Journal of Global Optimization, Springer, vol. 55(1), pages 27-51, January.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:1:p:27-51
    DOI: 10.1007/s10898-011-9811-1
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    References listed on IDEAS

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    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. L. C. Zeng & J. C. Yao, 2007. "Existence Theorems for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 321-337, February.
    3. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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