A Fixed Point Approach to Stability of k-$$\text {th}$$ Radical Functional Equation in Non-Archimedean $$(n,\beta )$$-Banach Spaces

Abstract

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: $$\begin{aligned} f\left( \root k \of {x^k+y^k}\right) = f(x)+f(y), \end{aligned}$$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.