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The Levitin-Polyak well-posedness by perturbations for systems of general variational inclusion and disclusion problems |
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| Authors: | J. W. Chen Y. J. Cho S. A. Khan Z. Wan C. F. Wen |
| Affiliation: | 1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China 2. Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, Korea 3. Department of Mathematics, BITS-Pilani, Dubai Campus, Dubai, 345055, UAE 4. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China 5. Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan |
| Abstract: | In this paper, the notions of the Levitin-Polyak well-posedness by perturbations for system of general variational inclusion and disclusion problems (shortly, (SGVI) and (SGVDI)) are introduced in Hausdorff topological vector spaces. Some sufficient and necessary conditions of the Levitin-Polyak well-posedness by perturbations for (SGVI) (resp., (SGVDI)) are derived under some suitable conditions. We also explore some relations among the Levitin-Polyak well-posedness by perturbations, the existence and uniqueness of solution of (SGVI) and (SGVDI), respectively. Finally, the lower (upper) semicontinuity of the approximate solution mappings of (SGVI) and (SGVDI) are established via the Levitin-Polyak well-posedness by perturbations. |
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