chebyshev sets
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2021 ◽  
Vol 212 (5) ◽  
Author(s):  
Alexey Rostislavovich Alimov ◽  
Borislav Borusovich Bednov

2019 ◽  
Vol 107 (3) ◽  
pp. 289-301
Author(s):  
THEO BENDIT

The Chebyshev conjecture posits that Chebyshev subsets of a real Hilbert space $X$ are convex. Works by Asplund, Ficken and Klee have uncovered an equivalent formulation of the Chebyshev conjecture in terms of uniquely remotal subsets of $X$. In this tradition, we develop another equivalent formulation in terms of Chebyshev subsets of the unit sphere of $X\times \mathbb{R}$. We characterise such sets in terms of the image under stereographic projection. Such sets have superior structure to Chebyshev sets and uniquely remotal sets.


Optimization ◽  
2019 ◽  
Vol 68 (8) ◽  
pp. 1599-1624
Author(s):  
Xian-Fa Luo ◽  
Li Meng ◽  
Ching-Feng Wen ◽  
Jen-Chih Yao

Author(s):  
H. R. Goudarzi

AbstractThe main aim of this paper is to present some basic as well as essential results involving the notion of p-Chebyshev sets in probabilistic normed spaces. In particular, we discuss the convexity of p-Chebyshev sets, decomposition of the space into its special subspaces, and we see a characterization of p-Chebyshev sets in quotient spaces.


2018 ◽  
Vol 73 (2) ◽  
pp. 366-368 ◽  
Author(s):  
A. R. Alimov ◽  
E. V. Shchepin
Keyword(s):  

2017 ◽  
Vol 26 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Warren B. Moors
Keyword(s):  

2016 ◽  
Vol 207 ◽  
pp. 265-282 ◽  
Author(s):  
David Ariza-Ruiz ◽  
Aurora Fernández-León ◽  
Genaro López-Acedo ◽  
Adriana Nicolae

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