Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds

被引：88

作者：

Li, Chong ^{[2
]}

Lopez, Genaro ^{[1
]}

Martin-Marquez, Victoria ^{[1
]}

Wang, Jin-Hua ^{[3
]}

机构：

[1] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[3] Zhejiang Univ Technol, Dept Math, Hangzhou 310032, Zhejiang, Peoples R China

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2011年 / 19卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Hadamard manifold; Firmly nonexpansive mapping; Resolvent; Yosida approximation; Maximal monotone vector field; Pseudo-contractive mapping; STRONG-CONVERGENCE THEOREMS; PROXIMAL POINT ALGORITHM; ASYMPTOTIC-BEHAVIOR; ACCRETIVE-OPERATORS; VARIATIONAL-INEQUALITIES; COACCRETIVE OPERATORS; NONEXPANSIVE-MAPPINGS; BANACH; EXISTENCE; ZEROS;

D O I：

10.1007/s11228-010-0169-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Firmly nonexpansive mappings are introduced in Hadamard manifolds, a particular class of Riemannian manifolds with nonpositive sectional curvature. The resolvent of a set-valued vector field is defined in this setting and by means of this concept, a strong relationship between monotone vector fields and firmly nonexpansive mappings is established. This fact is then used to prove that the resolvent of a maximal monotone vector field has full domain. The Yosida approximation of a set-valued vector field is also introduced, analyzing its properties from which the asymptotic behavior of the resolvent is studied. Regarding the singularities of a set-valued monotone vector field, existence results are proved under certain boundary condition. As a consequence, the existence of fixed points for continuous pseudo-contractive mappings is obtained.

引用

页码：361 / 383

页数：23

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