Near convexity, near smoothness and approximative compactness of half spaces in Banach spaces

2016 ◽  
Vol 32 (5) ◽  
pp. 599-606
Author(s):  
Zi Hou Zhang ◽  
Yu Zhou ◽  
Chun Yan Liu
Keyword(s):  
Banach Spaces ◽  
Approximative Compactness

Approximative compactness and continuity of metric projector in Banach spaces and applications

2008 ◽  
Vol 51 (2) ◽  
pp. 293-303 ◽  
Author(s):  
ShuTao Chen ◽  
Henryk Hudzik ◽  
Wojciech Kowalewski ◽  
YuWen Wang ◽  
Marek Wisła
Keyword(s):  
Banach Spaces ◽  
Approximative Compactness

scholarly journals Characterization of approximative compactness in Banach spaces

2015 ◽  
Vol 45 (12) ◽  
pp. 1953-1960
Author(s):  
Yu ZHOU ◽  
ChunYan LIU ◽  
ZiHou ZHANG
Keyword(s):  
Banach Spaces ◽  
Approximative Compactness

Nearly dentability and approximative compactness and continuity of metric projector in Banach spaces

2011 ◽  
Vol 41 (9) ◽  
pp. 815-825 ◽  
Author(s):  
YunAn CUI ◽  
ShaoQiang SHANG ◽  
YongQiang FU
Keyword(s):  
Banach Spaces ◽  
Approximative Compactness

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 Approximative Compactness and Radon-Nikodym Property inw∗Nearly Dentable Banach Spaces and Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Shaoqiang Shang ◽  
Yunan Cui
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Generalized Inverse ◽  
Orlicz Function ◽  
Function Spaces ◽  
Inverse Theory ◽  
Nikodym Property ◽  
Projector Operator ◽  
Approximative Compactness

Authors definew∗nearly dentable Banach space. Authors study Radon-Nikodym property, approximative compactness and continuity metric projector operator inw∗nearly dentable space. Moreover, authors obtain some examples ofw∗nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications ofw∗nearly dentability in generalized inverse theory of Banach space.

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