2016-07-222016-07-222012-02Espínola García, R. y Nicolae, A. (2012). Mutually nearest and farthest points of sets and the Drop Theorem in geodesic spaces. Monatshefte für Mathematik, 165 (2), 173-197.0026-92551436-5081http://hdl.handle.net/11441/43923Let A and X be nonempty, bounded and closed subsets of a geodesic metric space (E, d). The minimization (resp. maximization) problem denoted by min(A, X) (resp. max(A, X)) consists in finding (a0,x0)∈A×X(a0,x0)∈A×X such that d(a0,x0)=inf{d(a,x):a∈A,x∈X}d(a0,x0)=inf{d(a,x):a∈A,x∈X} (resp. d(a0,x0)=sup{d(a,x):a∈A,x∈X}d(a0,x0)=sup{d(a,x):a∈A,x∈X}). We give generic results on the well-posedness of these problems in different geodesic spaces and under different conditions considering the set A fixed. Besides, we analyze the situations when one set or both sets are compact and prove some specific results for CAT(0) spaces. We also prove a variant of the Drop Theorem in Busemann convex geodesic spaces and apply it to obtain an optimization result for convex functions.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Best approximationMinimization problemMaximization problemWell-posednessGeodesic spaceDrop Theoreminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1007/s00605-010-0266-0https://idus.us.es/xmlui/handle/11441/43923