Measures of Weak Compactness and Fixed Point Theory

Details Measures of Weak Compactness and Fixed Point Theory Measures of Weak Compactness and Fixed Point Theory

2003-10-27

arxiv.org/abs/math/0310422v2

Mathematics

Functional Analysis

9 pages

Scientific paper

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.

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