Artículo
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces
Autor/es | Fernández León, Aurora
Nicolae, Adriana |
Departamento | Universidad de Sevilla. Departamento de Didáctica de las Matemáticas |
Fecha de publicación | 2014 |
Fecha de depósito | 2016-07-04 |
Publicado en |
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Resumen | Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is
relatively nonexpansive if d(T x, T y) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point
for such a mapping is a point x ∈ A ∪ ... Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively nonexpansive if d(T x, T y) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, T x) = dist(A,B). In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171, 283–293 (2005)] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in A × B of a pair of best proximity points. |
Cita | Fernández León, A. y Nicolae, A. (2014). Best proximity pair results for relatively nonexpansive mappings in geodesic spaces. Numerical functional analysis and optimization, 35 (11), 1399-1418. |
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