Geometric Properties of Banach Spaces and the Existence of Nearest and Farthest Points
نویسنده
چکیده
The aim of this paper is to present some existence results for nearest-point and farthestpoint problems, in connection with some geometric properties of Banach spaces. The idea goes back to Efimov and Stečkin who, in a series of papers (see [28, 29, 30, 31]), realized for the first time that some geometric properties of Banach spaces, such as strict convexity, uniform convexity, reflexivity, and the Kadec-Klee property, and so forth, characterize some generic results concerning the uniqueness and existence of nearest points. Let X be a real normed linear space and Z a nonempty subset of X . For x ∈ X , put
منابع مشابه
w_0-Nearest Points and w_0-Farthest Point in Normed Linear Spaces
w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces
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