Well-posedness by perturbations of mixed variational inequalities in Banach spaces |
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Authors: | Ya-Ping Fang Nan-Jing Huang Jen-Chih Yao |
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Institution: | 1. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, ROC |
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Abstract: | In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-posedness by perturbations. We also show that under suitable conditions, the well-posedness by perturbations of a mixed variational inequality problem is equivalent to the well-posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution. |
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Keywords: | Mixed variational inequality Inclusion problem Fixed point problem Well-posedness by perturbation Uniqueness |
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