A Fixed Point Approach to Stability of k-th Radical Functional Equation in Non-Archimedean (n, β)-Banach Spaces

In this work, we prove a simple fixed point theorem in non-Archimedean (n,beta)\-Banach spaces, by applying this fixed point theorem, we will study the stability and the hyperstability of the kth radical-type functional equation: where f is a mapping on the set of real numbers and k is a fixed positive integer. Furthermore, we give some important consequences from our main results.

Automated summary

In this work, a simple fixed point theorem in non-Archimedean (n, beta)-Banach spaces is proved and applied to studying the stability and hyperstability of the kth radical-type functional equation. Some important consequences are also derived from the main results.