Measures of weak noncompactness, nonlinear Leray-Schauder alternatives in Banach algebras satisfying condition (<i>P</i>) and an application

Abstract

In this paper, we establish some new nonlinear Leray-Schauder alternatives for the sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. As an application, our results are used to prove the existence of solutions for a nonlinear
integral equation.

Keywords: Measures of weak noncompactness, weakly condensing, weakly sequentially continuous, fixed point theorems, integral equation