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.

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 Approximative compactness and continuity of metric projections

1974 ◽  
Vol 11 (1) ◽  
pp. 47-55 ◽  
Author(s):  
B.B. Panda ◽  
O.P. Kapoor
Keyword(s):  
Large Class ◽  
Banach Spaces ◽  
Metric Space ◽  
Metric Projection ◽  
Uniformly Convex ◽  
Chebyshev Set ◽  
Approximatively Compact ◽  
Metric Projections ◽  
Uniformly Convex Spaces ◽  
Approximative Compactness

In the paper “Some remarks on approximative compactness”, Rev. Roumaine Math. Pures Appl. 9 (1964), Ivan Singer proved that if K is an approximatively compact Chebyshev set in a metric space, then the metric projection onto K is continuous. The object of this paper is to show that though, in general, the continuity of the metric projection supported by a Chebyshev set does not imply that the set is approximatively compact, it is indeed so in a large class of Banach spaces, including the locally uniformly convex spaces. It is also proved that in such a space X the metric projection onto a Chebyshev set is continuous on a set dense in X.

scholarly journals The bargaining set for almost-convex games

2012 ◽  
Vol 225 (1) ◽  
pp. 83-89
Author(s):  
Jesús Getán ◽  
Josep M. Izquierdo ◽  
Jesús Montes ◽  
Carles Rafels
Keyword(s):  
Convex Games ◽  
Bargaining Set ◽  
Almost Convex

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.

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