Uniformly-like convex solutions for the polynomial-like iterative equation in Banach spaces

Abstract

Using Schauder’s fixed point theorem and the Banach contraction principle, the existence, uniqueness, and stability of monotone solutions and uniformly-like convex solutions of the polynomial-like iterative functional equation are studied in Banach spaces. Furthermore, the approximate solutions of the corresponding solutions are considered. Some examples are considered for our results.