含参广义向量拟均衡问题有效解映射的下半连续性

2020-11-27 08:56孟旭东
关键词:旭东连续性广义

孟旭东

含参广义向量拟均衡问题有效解映射的下半连续性

孟旭东

(南昌航空大学科技学院,江西,南昌 330034)

针对一类含参广义向量拟均衡问题,在实Hausdorff拓扑向量空间中研究了有效解映射的下半连续性。在锥凹、一致连续及Hausdorff上半连续的假设下,运用分析的方法,得到了含参广义向量拟均衡问题有效解映射下半连续性定理。

有效解映射;下半连续性;含参广义向量拟均衡问题

向量优化、向量变分不等式、向量Nash平衡及向量补问题等均是向量均衡问题研究的热点问题。文献[1-3]主要讨论了向量均衡问题解的存在性。文献[4-13]重点围绕向量均衡问题解的稳定性进行分析,主要研究了解映射的下半连续性。文献[4-11]运用标量化方法、稠密性结果、凸分析及光滑分析等研究了含参(集值)向量均衡问题各种有效解映射的下半连续性。在锥凹及一致连续的条件下,Rabian,Panatda和Pakkapon在文献[12]中,运用标量化方法,讨论了含参广义向量均衡问题近似解映射的下半连续性。在文献[13]中,Han和Gong得到了含参广义强向量均衡问题有效解映射下半连续性定理。

受文献[12]与文献[13]思想的启发,在实Hausdorff拓扑向量空间中,研究含参广义向量拟均衡问题的有效解映射的下半连续性。通过转化为集值映射在零点下半连续的方法,给出含参广义向量拟均衡问题有效解映射下半连续的最优性条件。

1 预备知识

其中

为给定集值映射,满足

2 主要结果

定理 假设以下条件成立:

2.3 不同ADC值下肺结节良恶性分布情况 以ADC=1.41×10-3m2/s为临界值分析肺结节良恶性分布情况,结果显示,ADC<1.41×103 m2/s恶性病变的发生例数明显高于良性病变,而ADC≥1.41×103 m2/s的良性病变的发生例数明显高于恶性病变,见表3。

再由(5)知,

再由(12)与(13)知,

再由(10)知,

再由(2)、(9)与(16)知,

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LOWER SEMI-CONTIONUITY OF EFFICIENT SOLUTION MAPPING TO PARAMETRIC GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS

MENG Xu-dong

(Science College of Nanchang Hang kong University,Nanchang, Jiangxi, 330034,China)

The lower semi-continuity of efficient solution mapping to a class of parametric generalized vector quasi-equilibrium problems in real Hausdorff topological vector space is studied.Under the assumption conditions of cone concave,uniformly continuous and Hausdorff upper semi-continuous, the lower semi-continuity theorem for efficient solution mapping to the parametric generalized vector quasi-equilibrium problems is gained by using the method of analysis.

efficient solution mapping; lower semicontionuity; parametric generalized vector quasi-equilibrium problems

O317

A

10.3969/j.issn.1674-8085.2020.05.001

1674-8085(2020)05-0001-04

2020-05-08;

2020-06-15

国家自然科学基金项目(11201216);江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614);江西省教育厅科学技术研究项目(GJJ161597)

孟旭东(1982-),男,江西南昌人,副教授,硕士,主要从事向量均衡与向量优化理论研究(E-mail: mxudongm@163.com).

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