Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 80987, 14 pages
doi:10.1155/2007/80987
Research Article

Remarks on Separation of Convex Sets, Fixed-Point Theorem, and Applications in Theory of Linear Operators

Kamal N. Soltanov

 Department of Mathematics, Faculty of Sciences, Hacettepe University, Beytepe, Ankara 06532, Turkey
Received 20 February 2007; Accepted 2 May 2007

Recommended by Simeon Reich

Abstract

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.