Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on Lp(R+)

摘要

Let Lp(R+) denote the space of Lebesgue integrable functions on R+ with the standard norm ∥x∥p=(∫0∞|x(t)|pdt)1p.First, we define a new measure of noncompactness on the spaces Lp(R+) (1 ≤ p < ∞). In addition, we study the existence of entire solutions for a class of nonlinear functional integral equations of convolution type using Darbo’s fixed point theorem, which is associated with the new measure of noncompactness. We provide some examples to demonstrate that our results are applicable whereas the previous results are not.