In this work, we prove a simple fixed point theorem in non-Archimedean (n,β)-Banach spaces, by applying this fixed point theorem, we will study the stability and the hyperstability of the kth radical-type functional equation f(k√x^k+y^k)=f(x)+f(y) 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
