Well-Posedness for Mixed Quasivariational-Like Inequalities |
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| Authors: | L. C. Ceng N. Hadjisavvas S. Schaible J. C. Yao |
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| Affiliation: | (1) Department of Mathematics, Shanghai Normal University, Shanghai, China;(2) Department of Product and Systems Design Engineering, University of the Aegean, Hermoupolis, Syros, Greece;(3) A.G. Anderson Graduate School of Management, University of California, Riverside, CA, USA;(4) Department of Applied Mathematics, National Sun-Yat-Sen University, Kaohsiung, Taiwan |
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| Abstract: | In this paper, we introduce concepts of well-posedness, and well-posedness in the generalized sense, for mixed quasivariational-like inequalities where the underlying map is multivalued. We give necessary and sufficient conditions for the various kinds of well-posedness to occur. Our results generalize and strengthen previously found results for variational and quasivariational inequalities. Part of this research was done while the second and the third authors were visiting the Department of Applied Mathematics, National Sun-Yat-Sen University. The authors wish to thank the Department for its hospitality. |
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| Keywords: | Mixed quasivariational-like inequalities Well-posedness Well-posedness in the generalized sense Multivalued maps Measure of noncompactness |
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