Almost Chebyshev set with respect to bounded subsets

1997 ◽  
Vol 40 (4) ◽  
pp. 375-383 ◽  
Author(s):  
Chong Li ◽  
Xinghua Wang
Keyword(s):  
Chebyshev Set

scholarly journals Suns are convex in tangent directions

2019 ◽  
Vol 484 (2) ◽  
pp. 131-133
Author(s):  
A. R. Alimov ◽  
E. V. Shchepin
Keyword(s):  
Linear Space ◽  
Unit Sphere ◽  
Normed Linear Space ◽  
Tangent Line ◽  
Chebyshev Set ◽  
Tangent Direction

A direction d is called a tangent direction to the unit sphere S of a normed linear space s  S and lin(s + d) is a tangent line to the sphere S at s imply that lin(s + d) is a one-sided tangent to the sphere S, i. e., it is the limit of secant lines at s. A set M is called convex with respect to a direction d if [x, y]  M whenever x, y in M, (y - x) || d. We show that in a normed linear space an arbitrary sun (in particular, a boundedly compact Chebyshev set) is convex with respect to any tangent direction of the unit sphere.

scholarly journals A $2$-parameter Chebyshev set which is not a sun

1975 ◽  
Vol 50 (1) ◽  
pp. 315-315
Author(s):  
Charles B. Dunham
Keyword(s):  
Chebyshev Set

scholarly journals A connected separable metric space with a dispersed Chebyshev set

1983 ◽  
Vol 39 (4) ◽  
pp. 320-323 ◽  
Author(s):  
Susanna Papadopoulou
Keyword(s):  
Metric Space ◽  
Chebyshev Set ◽  
Separable Metric Space

A monotone path connected Chebyshev set is a sun

2012 ◽  
Vol 91 (1-2) ◽  
pp. 290-292 ◽  
Author(s):  
A. R. Alimov
Keyword(s):  
Chebyshev Set ◽  
Monotone Path ◽  
Path Connected

scholarly journals A note on suns in convex metric spaces

2010 ◽  
Vol 87 (101) ◽  
pp. 139-142
Author(s):  
T.D. Narang ◽  
R. Sangeeta
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Metric Projection ◽  
Convex Metric Space ◽  
Chebyshev Set ◽  
Almost Convex ◽  
Convex Metric Spaces ◽  
Lower Semi ◽  
Existence Set

We prove that in a convex metric space (X,d), an existence set K having a lower semi continuous metric projection is a ?-sun and in a complete M-space, a Chebyshev set K with a continuous metric projection is a ?-sun as well as almost convex.

scholarly journals On δ-suns

2008 ◽  
Vol 83 (97) ◽  
pp. 99-104 ◽  
Author(s):  
T.D. Narang ◽  
Shavetambry Tejpal
Keyword(s):  
Chebyshev Set ◽  
Almost Convex ◽  
Approximatively Compact

We prove that an approximatively compact Chebyshev set in an M-space is a ?-sun and a ?-sun in a complete strong M-space (or externally convex M-space) is almost convex.

CHEBYSHEV SETS

2014 ◽  
Vol 98 (2) ◽  
pp. 161-231 ◽  
Author(s):  
JAMES FLETCHER ◽  
WARREN B. MOORS
Keyword(s):  
Linear Space ◽  
Product Space ◽  
Normed Linear Space ◽  
Sufficient Conditions ◽  
Metric Projection ◽  
Inner Product Space ◽  
Inner Product ◽  
Best Approximations ◽  
Chebyshev Set ◽  
Chebyshev Sets

AbstractA Chebyshev set is a subset of a normed linear space that admits unique best approximations. In the first part of this paper we present some basic results concerning Chebyshev sets. In particular, we investigate properties of the metric projection map, sufficient conditions for a subset of a normed linear space to be a Chebyshev set, and sufficient conditions for a Chebyshev set to be convex. In the second half of the paper we present a construction of a nonconvex Chebyshev subset of an inner product space.

An N-Parameter Chebyshev Set which is not a Sun

1975 ◽  
Vol 18 (4) ◽  
pp. 489-492 ◽  
Author(s):  
Dietrich Braess
Keyword(s):  
Chebyshev Set ◽  
Chebyshev Sets ◽  
Isolated Point

Recently, Dunham has given examples for 1-parameter and 2-parameter Chebyshev sets which are not suns. In this note 2-parameter sets with these properties are described.When studying the old problem whether Chebyshev sets are always convex, Klee [10] introduced certain sets which were called suns by Efimov and Stechkin [7]. Recently, in two shorts notes Dunham [4, 5] has given examples of 1-parameter- and 2-parameter-sets which are Chebyshev sets but not suns (cf. also [3]). The examples refer to Chebyshev sets in containing an isolated point.

scholarly journals A Chebyshev Set and its Distance Function

2002 ◽  
Vol 119 (2) ◽  
pp. 181-192 ◽  
Author(s):  
Zili Wu
Keyword(s):  
Distance Function ◽  
Chebyshev Set

scholarly journals Closure in a Hilbert space of a prehilbert space Chebyshev set

2005 ◽  
Vol 153 (2-3) ◽  
pp. 239-244 ◽  
Author(s):  
Gordon G. Johnson
Keyword(s):  
Hilbert Space ◽  
Chebyshev Set
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