链完备偏序集上广义向量均衡问题解映射的保序性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1483-1491.

链完备偏序集上广义向量均衡问题解映射的保序性

王月虎^1,*(),刘保庆²

¹ 南京财经大学管理科学与工程学院南京 210023
² 南京财经大学应用数学学院南京 210023

收稿日期:2018-08-30 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 王月虎 E-mail:wyhmath@163.com
基金资助:
江苏高校哲学社会学研究项目(2017SJB0238);江苏省高校自然科学研究面上项目(16KJB110009);江苏省自然科学基金项目(BK20171041)

Order-Preservation of Solution Correspondence for Generalized Vector Equilibrium Problems on Chain-Complete Posets

Yuehu Wang^1,*(),Baoqing Liu²

¹ School of Management Science and Engineering, Nanjing University of Finance and Economics, Nanjing 210023
² School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023

Received:2018-08-30 Online:2019-12-26 Published:2019-12-28
Contact: Yuehu Wang E-mail:wyhmath@163.com
Supported by:
the Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province(2017SJB0238);the Natural Science Foundation in Colleges and Universities in Jiangsu Province(16KJB110009);the Natural Science Foundation in Jiangsu Province(BK20171041)

摘要/Abstract

摘要：

在链完备偏序集上研究了一类参数广义向量均衡问题解映射的上保序性.与已有关注向量均衡问题解的存在性、拓扑连续性和迭代算法的研究相比，保序性是一个全新的课题，它对分析均衡解的变化趋势具有重要意义.由于主要研究工具为序不动点定理和保序选择定理，获得的结果不再要求相关映射具有任何凸性和连续性.

关键词: 链完备偏序集, 广义向量均衡问题, 不动点定理, 保序性

Abstract:

In this paper, we explore the upper order-preservation of solution correspondence for parametric generalized vector equilibrium problems on chain-complete posets. In contrast to the previous results which mainly focus on the existence, topological continuity and algorithms, the order-preservation is a new subject for generalized vector equilibrium problems and it is useful for predicting the changing trend of solutions. Since our approaches are order-theoretic fixed point theorems and isotone selection theorems, neither convexity nor continuity is required for the mapping F.

Key words: Chain-complete poset, Generalized vector equilibrium problems, Fixed point theorem, Order-preservation

中图分类号:

王月虎,刘保庆. 链完备偏序集上广义向量均衡问题解映射的保序性[J]. 数学物理学报, 2019, 39(6): 1483-1491.

Yuehu Wang,Baoqing Liu. Order-Preservation of Solution Correspondence for Generalized Vector Equilibrium Problems on Chain-Complete Posets[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1483-1491.

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