Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (3): 263-274.doi: https://doi.org/10.1007/s10483-009-0301-z

• Articles •    下一篇

Systems of variational inclusions and optimization problems in locally FC-uniform spaces

Xie-ping DING   

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China
  • 收稿日期:2008-09-24 修回日期:2009-01-14 出版日期:2009-03-05 发布日期:2009-03-01
  • 通讯作者: http://baike.baidu.com/view/1087533.htm

Systems of variational inclusions and optimization problems in locally FC-uniform spaces

Xie-ping DING   

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China
  • Received:2008-09-24 Revised:2009-01-14 Online:2009-03-05 Published:2009-03-01
  • Contact: http://baike.baidu.com/view/1087533.htm

摘要: In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

关键词: Himmelberg type fixed point theorem, system of generalized vector optimization problems, locally FC-uniform space, system of generalized vector quasi-variational inclusions, KKM type theorem

Abstract: In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

Key words: KKM type theorem, Himmelberg type fixed point theorem, system of generalized vector quasi-variational inclusions, system of generalized vector optimization problems, locally FC-uniform space

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