| 孟旭东.含参集值向量拟均衡问题和对偶问题解Lipschitz连续性[J].,2022,62(3):321-330 |
| 含参集值向量拟均衡问题和对偶问题解Lipschitz连续性 |
| Lipschitz continuity of solutions for parametric set-valued vector quasi-equilibrium problems and dual problems |
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| DOI：10.7511/dllgxb202203012 |
| 中文关键词: 含参集值向量拟均衡问题 解 集值映射 Lipschitz连续性 |
| 英文关键词: parametric set-valued vector quasi-equilibrium problems solution set-valued mapping Lipschitz continuity |
| 基金项目:江西省教育厅科学技术重点研究项目(GJJ181565GJJ191614GJJ218701)；南昌航空大学校级重点科学技术研究项目(KJKT2108). |
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| 中文摘要: |
| 在赋范线性空间中研究一类含参集值向量拟均衡问题和对偶问题解的Lipschitz连续性．提出含参集值向量拟均衡问题和对偶问题解的概念，在约束函数具有Lipschitz一致连续性基本假设条件下，运用分析方法建立含参集值向量拟均衡问题和对偶问题解的Lipschitz连续的充分性定理，并给出适当的例子来说明所得结果的有效性．借助理论成果可进一步研究含参集值向量拟均衡问题解的连通性、对偶性及近似计算等． |
| 英文摘要: |
| Lipschitz continuity of solutions for a class of parametric set-valued vector quasi-equilibrium problems and dual problems is studied in normed linear spaces. The concepts for parametric set-valued vector quasi-equilibrium problems and dual problems are proposed. Under the basic assumption that the constraint function has Lipschitz uniform continuity, the Lipschitz continuity sufficient theorems of solutions to parametric set-valued vector quasi-equilibrium problems and dual problems are established by using the analytical method. The appropriate examples are given to illustrate the effectiveness of the results. With the help of theoretical results, the connectivity, duality and approximate calculation of solutions to parametric set-valued vector quasi-equilibrium problems can be further studied. |
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