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An existence result for generalized vector equilibrium problems without pseudomonotonicity |
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| Authors: | Lu-Chuan Zeng Jen-Chih Yao |
| Institution: | aDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, China bDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan |
| Abstract: | In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given. |
| Keywords: | Generalized vector equilibrium problem Generalized vector variational-like inequalities KKM-map Hausdorff metric |
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