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Nonexpansive mappings and monotone vector fields in Hadamard manifolds

Opened Access Nonexpansive mappings and monotone vector fields in Hadamard manifolds
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Autor: Martín Márquez, Victoria
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2009
Publicado en: Communications in Applied Analysis, 13 (4), 633-646.
Tipo de documento: Artículo
Resumen: This paper briefly surveys some recent advances in the investigation of nonexpansive mappings and monotone vector fields, focusing in the extension of basic results of the classical nonlinear functional analysis from Banach spaces to the class of nonpositive sectional curvature Riemannian manifolds called Hadamard manifolds. Within this setting, we first analyze the problem of finding fixed points of nonexpansive mappings. Later on, different classes of monotonicity for set-valued vector fields and the relationship between some of them will be presented, followed by the study of the existence and approximation of singularities for such vector fields. We will discuss about variational inequality and minimization problems in Hadamard manifolds, stressing the fact that these problems can be solved by means of the iterative approaches for monotone vector fields.
Cita: Martín Márquez, V. (2009). Nonexpansive mappings and monotone vector fields in Hadamard manifolds. Communications in Applied Analysis, 13 (4), 633-646.
Tamaño: 160.8Kb
Formato: PDF

URI: http://hdl.handle.net/11441/48956

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