Existence and uniqueness of best proximity points in geodesic metric spaces |
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Authors: | Aurora Fernández-León |
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Institution: | Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P.O.Box: 1160, 41080 Sevilla, Spain |
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Abstract: | A mapping T:A∪B→A∪B such that T(A)⊆B and T(B)⊆A is called a cyclic mapping. A best proximity point x for such a mapping T is a point such that d(x,Tx)= dist(A,B). In this work we provide different existence and uniqueness results of best proximity points in both Banach and geodesic metric spaces. We improve and extend some results on this recent theory and give an affirmative partial answer to a recently posed question by Eldred and Veeramani in A.A. Eldred, P. Veeramani Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2) (2006) 1001-1006]. |
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Keywords: | primary 54E40 54E35 54H25 secondary 47H10 |
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