【作者】 孔德洲；

【导师】 丁协平；

【作者基本信息】 四川师范大学 ， 运筹学与控制论， 2005， 硕士

【摘要】 本文研究了不动点定理及其应用和变分不等式解的算法。在第一章中,研究了零调映象,在乘积拓扑矢量空间中得到了一集值映象簇的不动点定理,给出了对广义矢量平衡问题组的应用。在第二章中,在G ?凸空间中证明了关于较好允许映象的新的不动点和极大元定理,作为应用,得到了一些抽象经济的平衡存在定理。在第三章中,研究了混合变分不等式,在无限维Hilbert 空间内借助于极大单调算子的ε?扩大提出了分裂惯性近似算法并证明了算法的弱收敛性。更多还原

【Abstract】 This paper is concerned with fixed point theorems and their applications and algorithm of variational inequalities. In chapter one, acyclic mappings is discussed. Some new fixed point theorems for a family of set-valued mappings in product space of topological vector spaces are obtained. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are established. Chapter two, some new collectively fixed point theorems and existence theorems of maximal element involving better admissible mappings in G ?convex spaces are proved. As applications some equilibrium existence theorems of abstract economies are obtained. In chapter three, a class of mixed variational inequalities is studied. By using the ε?enlargements of maximal monotone operators, we get a splitting inertial proximal algorithm. Moreover, we also prove the weak convergence criteria.更多还原