Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Weakly sequentially complete Banach spaces
  • directional derivatives of cone convex mappings
  • cone convex mappings
  • directional derivatives

Mathematics Subject Classification

26A51, 06A06, 46B45, 46B40

Suggested citation

E. M. Bednarczuk, K. Lesniewski. “On Weakly Sequentially Complete Banach Spaces.” Journal of Convex Analysis 24 (2017), No. 4, 1341–1356.

Copyright Heldermann Verlag 2017