Survey on Ulam Stability with Respect to n-Norms and (n, β)-Norms

This article is a survey of the results published so far on Ulam stability of functional equations in n-normed spaces and (n, β)-normed spaces. We present and examine them, highlighting some traps they contain and outlining potential straightforward generalizations. We also draw attention to certain symmetries present in the results discussed. In this way, we complement two earlier surveys on Ulam stability in two-normed spaces.