positive periodic solutions for a neutral differential equation with iterative terms arising in biology and population dynamics

In this article, a class of first order neutral delay differential equations with iterative terms is investigated. the proofs of the existence of positive periodic solutions rely on the krasnoselskii’s fixed point theorem together with the green’s functions method. furthermore, by the aid of the banach fixed point theorem and under an extra condition, we establish the existence, uniqueness and stability results. we provide an example to show the accuracy of the conditions of the obtained findings which extend and generalize earlier ones in the literature.