On mutually nearest and mutually furthest points of sets in Banach spaces
نویسندگان
چکیده
منابع مشابه
Porosity of mutually nearest and mutually furthest points in Banach spaces
Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X : Let BðX Þ (resp. KðXÞ) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fAABðX Þ : A-G 1⁄4 |g and KGðX Þ 1⁄4 BGðX Þ-KðXÞ: We introduce the admissible family A of BðX Þ...
متن کاملOn Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let K(X) denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let KG(X) denote the closure of the set {A ∈ K(X) : A∩G = ∅}. We prove that the set of all A ∈ KG(X) (resp. A ∈ K(X)), such that the minimizat...
متن کاملOn Almost Well-posed Mutually Nearest and Mutually Furthest Point Problems
Let G be a nonempty closed (resp. bounded closed) subset in a strongly convex Banach space X. Let BðXÞ denote the space of all nonempty bounded closed subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fA 2 BðXÞ : A \ G 1⁄4 ;g. We prove that E(G) (resp. Eo(G)), the set of all A 2 BGðXÞ (resp. A 2 BðXÞ) such that the minimization (resp. maximization) pro...
متن کاملMutually Compactificable Topological Spaces
Two disjoint topological spaces X , Y are (T2-) mutually compactificable if there exists a compact (T2-) topology on K = X ∪ Y which coincides on X , Y with their original topologies such that the points x ∈ X , y ∈ Y have open disjoint neighborhoods in K . This paper, the first one from a series, contains some initial investigations of the notion. Some key properties are the following: a topol...
متن کاملNearest Points and Delta Convex Functions in Banach Spaces
Given a closed set C in a Banach space (X, ‖ · ‖), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ‖x − z‖, where dC is the distance of x from C. We shortly survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta-convex functions and indicate how it is related to finding neare...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1992
ISSN: 0021-9045
DOI: 10.1016/0021-9045(92)90082-y