On a functional-integral equation with deviating arguments

Abstract

We study the solvability of a functional-integral equation with deviating arguments, where our investigations take place in the space of Lebesgue integrable functions on an unbounded interval. In this space, we show that our functional-integral equation has at least one nonnegative and nonincreasing solution. The proof of our main result is based on a suitable combination of the technique associated with measures of noncompactness (in both the weak and the strong sense) and the Darbo fixed point. In the end, we conclude an example to illustrate our abstract results.