Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 1 (2017), 16-26.
Characterizations and applications of three types of nearly convex points
By using some geometric properties and nested sequence of balls, we prove seven necessary and sufficient conditions such that a point in the unit sphere of Banach space is a nearly rotund point of the unit ball of the bidual space. For any closed convex set and with , we give a series of characterizations such that is approximatively compact or approximatively weakly compact for by using three types of nearly convex points. Furthermore, making use of an S point, we present a characterization such that the convex subset is approximatively compact for some in . We also establish a relationship between nested sequence of balls and the approximate compactness of the closed convex subset for some .
Ann. Funct. Anal., Volume 8, Number 1 (2017), 16-26.
Received: 14 January 2016
Accepted: 17 May 2016
First available in Project Euclid: 14 October 2016
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Zhang, Zihou; Zhou, Yu; Liu, Chunyan. Characterizations and applications of three types of nearly convex points. Ann. Funct. Anal. 8 (2017), no. 1, 16--26. doi:10.1215/20088752-3720520. https://projecteuclid.org/euclid.afa/1476450344