Journal of Convex Analysis 24 (2017), No. 4, 1341--1356
Copyright Heldermann Verlag 2017
On Weakly Sequentially Complete Banach Spaces
Ewa M. Bednarczuk
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
and: Faculty of Mathematics and Information Science, University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
e.bednarczuk@mini.pw.edu.pl
Krzysztof Lesniewski
Faculty of Mathematics and Information Science, University of Technology, ul. Koszykowa 75, 00-662 Warsaw
k.lesniewski@mini.pw.edu.pl
We provide sufficient conditions for a Banach space Y to be weakly sequentially complete. These conditions are expressed in terms of the existence of directional derivatives for cone convex mappings with values in Y.
Keywords: Weakly sequentially complete Banach spaces, directional derivatives of cone convex mappings, cone convex mappings, directional derivatives.
MSC: 26A51, 06A06, 46B45, 46B40
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