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Keywords:
banach algebra; Furi–Pera condition; fixed point theorem; measure of noncompactness; integral equations
banach algebra; Furi–Pera condition; fixed point theorem; measure of noncompactness; integral equations
Summary:
In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is ${\mathcal D}$-Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].
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