A Generalization of Theorems Concerning a Nonlinear Functional Inequality in a Single Variable

Abstract

A generalization of a comparison theorem for the functional inequality

$$\psi \left[ {f\left( x \right)} \right] \leqslant g\left[ {x,\psi \left( x \right)} \right]$$

where ψ is an unknown function, is here presented. An application of this theorem to the theory of nonlinear functional equations is also given.