The behaviour of measures of noncompactness in $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R n ) with application to the solvability of functional integral equations

Abstract

In this work, we define a new measure of noncompactness on the space \(L^\infty ({\mathbb {R}}^n)\). In addition, we study the existence of solutions for a class of nonlinear functional integral equations of Fredholm type by using an extension of Darbo’s fixed point theorem associated with this new measure of noncompactness. Also, we will include an example which shows the efficiency of our results. The obtained results improve several ones obtained earlier.