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

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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).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lu-Chuan Ceng

  2. Scientific Computing Key Laboratory, Shanghai Universities, Shanghai, 200234, China

    Lu-Chuan Ceng

  3. Center for general Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

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  1. Lu-Chuan Ceng
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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Ceng, LC., Yao, JC. Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces. J Glob Optim 55, 27–51 (2013). https://doi.org/10.1007/s10898-011-9811-1

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  • DOI: https://doi.org/10.1007/s10898-011-9811-1

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