In this paper we study the existence of fixed points for the product of nonlinear operators. This kind of fixed points theorems is necessary in consideration of quadratic differential and integral problems. We concentrate on applicability of obtained theorems and we prove the existence of fixed points for operators acting on some function spaces being not necessarily Banach algebras. This result essentially extend earlier ones and can be successfully applied for all considered quadratic problems which will be also presented. © 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.2F2521529