Measures of Weak Compactness and Fixed Point Theory
Cleon S. Barroso, Donal O'Regan
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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