Comparison Theorem for a Functional Inequality

Abstract

Generalizing a result of E. Turdza (the case N = 2), the author here compares solutions of the functional inequality ψ^N(x) ≤ g(x) with solutions of the corresponding functional equation ψ^N(x) = g(x), in a prescribed class of functions, where g is a given function and ψ^N is the Nth iterate of the unknown function ψ.