Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds

被引:0
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作者
Chong Li
Genaro López
Victoria Martín-Márquez
Jin-Hua Wang
机构
[1] Zhejiang University,Department of Mathematics
[2] Universidad de Sevilla,Departamento de Análisis Matemático
[3] Zhejiang University of Technology,Department of Mathematics
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关键词
Hadamard manifold; Firmly nonexpansive mapping; Resolvent; Yosida approximation; Maximal monotone vector field; Pseudo-contractive mapping; 47H05; 49J40;
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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.
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页码:361 / 383
页数:22
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