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Measures of Weak Compactness and Fixed Point Theory

Cleon S. Barroso·Donal O'Regan
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Abstract

In this paper, we study a class of Banach spaces, called ϕ-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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BibTeXRIS

Cleon S. Barroso, Donal O'Regan. 2003-12-05. Measures of Weak Compactness and Fixed Point Theory. https://arxiv.org/abs/math/0310422

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