Positive solutions of nonlinear functional-integral equations

In this paper we study the conditions are required for existence of at least one positive solution of the functional-integral equation u (x) = g (x) + R h 0 k (x, s) F (u) (s)ds, x ∈ [0, h] where F : C [0, h] → C [0, h] is an operator. Our approach to the problem is based on the Krasnoselskii’s compression-expansion fixed point theorem.