Measures of Weak Compactness and Fixed Point Theory
Functional Analysis
2007-05-23 v2
Abstract
In this paper, we study a class of Banach spaces, called \phi-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous maps. A counter-example is given to justify our requirement. As an application, we establish an existence result for a Hammerstein integral equation in a Banach space.
Cite
@article{arxiv.math/0310422,
title = {Measures of Weak Compactness and Fixed Point Theory},
author = {Cleon S. Barroso and Donal O'Regan},
journal= {arXiv preprint arXiv:math/0310422},
year = {2007}
}
Comments
9 pages