Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 80987, 14 pages
Remarks on Separation of Convex Sets, Fixed-Point Theorem, and Applications in Theory of Linear Operators
Department of Mathematics, Faculty of Sciences, Hacettepe University, Beytepe, Ankara 06532, Turkey
Received 20 February 2007; Accepted 2 May 2007
Academic Editor: Simeon Reich
Copyright © 2007 Kamal N. Soltanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Some properties of the linear continuous operator and separation of convex subsets are investigated in this paper and a dual space for a subspace of a reflexive Banach space with a strictly convex norm is constructed. Here also an existence theorem and fixed-point theorem for general mappings are obtained. Moreover, certain remarks on the problem of existence of invariant subspaces of a linear continuous operator are given.