具有Q-函数的集值Ekeland变分原理的等价性

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英文篇名：Equivalence on Ekeland's variational principle via Q-function with set-valued maps 作者：万轩 英文作者：WAN Xuan;Basic Teaching Department,Chongqing Real Estate College;Department of Foundation,Chongqing Telecommunication Polytechnic College; 关键词：集值Ekeland变分原理 ; 集值Caristi-Kirk不动点定理 ; 集值Takahashi非凸极小化定理 ; 集值Oettli-Théra定理 ; 等价性 英文关键词：set-valued Ekeland's variational principle;;set-valued Caristi-Kirk's fixed point theorem;;set-valued Takahashi's nonconvex minimization theorem;;set-valued Oettli-Théra's theorem;;equivalence 中文刊名：NATR 英文刊名：Journal of Guizhou Normal University(Natural Sciences) 机构：重庆房地产职业学院基础教学部;重庆电讯职业学院基础部; 出版日期：2019-03-11 17:21 出版单位：贵州师范大学学报(自然科学版) 年：2019 期：v.37;No.144 基金：重庆市教委科学技术研究项目(No.KJ1605201) 语种：中文; 页：NATR201902010 页数：5 CN：02 ISSN：52-5006/N 分类号：63-67

摘要

根据各种Ekeland变分原理的等价形式,主要对在拟度量空间中所建立的具有Q-函数的集值Ekeland变分原理进行其等价性研究。首先根据在拟度量空间中所建立的具有Q-函数的集值Ekeland变分原理给出相应的集值形式的Caristi-Kirk不动点定理,Takahashi非凸极小化定理和Oettli-Théra定理,并给出证明。随后讨论新建立的集值形式的Caristi-Kirk不动点定理,Takahashi非凸极小化定理和Oettli-Théra定理与具有Q-函数的集值Ekeland变分原理之间的等价性。
        Equivalent forms based on various types of Ekeland's variational principle,the author considers the equivalence on Ekeland's variational principle via Q-function for set-valued maps in quasimetric spaces. Firstly,from a Ekeland's variational principle via Q-function for set-valued maps,a Caristi-Kirk's fixed point theorem,a Takahashi 's nonconvex minimization theorem and a OettliThéra's theorem for set-valued maps are deduced and proved. Furthermore,it is proved that some equivalences of the Ekeland's variational principle via Q-function with the Caristi-Kirk's fixed point theorems,the Takahashi's nonconvex minimization theorem and the Oettli-Théra's theorem for setvalued maps.

引文

[1]EKELAND I. On the variational principle[J]. Journal of Mathematical Analysis and Applications,1974,47(2):324-353.
    [2]EKELAND I. Nonconvex minimization problems[J]. Bulletin(New Series)of the American Mathematical Society,1979,1(3):443-474.
    [3]AL-HOMIDAN S,ANSARI Q H,YAO J C. Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory[J].Nonlinear Analysis,2008,69:126-139.
    [4]CHEN G Y,HUANG X X,HOU S H. General Ekeland's variational principle for set-valued mappings[J]. Journal of Optimization Theory and Applications,2000,106(1):151-164.
    [5]HA T X D. Some variants of the Ekeland variational principle for a set-valued map[J]. Journal of Optimization Theory and Applications,2005,124(1):187-206.
    [6]QIU J H. On Ha's version of set-valued Ekeland's variational principle[J]. Acta Mathematica Sinica,English Series,2012,28(4):717-726.
    [7]万轩,赵克全.关于局部凸空间中向量Eekland变分原理的等价性[J].运筹学学报,2013,17(3):124-128.
    [8]万轩,张万里,赵克全.基于改进集的集值Eekland变分原理[J].纯粹数学与应用数学,2015,31(6):567-574.
    [9]万轩,瞿先平,陈华峰.基于改进集的集值Ekeland变分原理的等价性[J].贵州师范大学学报(自然科学版),2016,34(6):70-73.
    [10]万轩,瞿先平.基于Q-函数的集值Ekeland变分原理[J].重庆师范大学学报(自然科学版),2017,34(5):6-11.
    [11]万轩.广义向量Ekeland变分原理及在向量优化中的应用[D].重庆:重庆师范大学,2013.