广义松弛拟单调变分不等式和平衡问题

发布时间：2018-02-11 19:31

  本文关键词： 变分不等式 广义松弛拟单调算子 广义松弛拟凸函数 平衡问题 广义松弛上半点性质　出处：《四川师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：本文在赋范空间中研究了集值映射的一种新的单调性,称之为广义松弛拟单调映射.运用KKM理论,在新引入的单调映射下我们证明了变分不等式的解集非空.同时,讨论了广义松弛拟凸函数与广义松弛拟单调映射之间的关系.此外,本文给出了当广义松弛拟单调映射具有广义松弛上半点性质时,对偶平衡问题解集非空,从而获得平衡问题解集非空.
[Abstract]:In this paper, we study a new monotonicity of set-valued mappings in normed spaces, which is called generalized relaxed quasi-monotone mappings. Using KKM's theory, we prove that the solutions of variational inequalities are nonempty under the newly introduced monotone mappings. The relationship between generalized relaxed quasiconvex functions and generalized relaxed quasi-monotone mappings is discussed. In addition, when generalized relaxed quasi-monotone mappings have the property of generalized relaxation upper half point, the solutions of dual equilibrium problems are not empty. Thus, the solution set of the equilibrium problem is not empty.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O178
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本文编号：1503823