Let \(U\subseteq \mathbb{R}^n\) be a nonempty convex set and let \(J\) be a real-valued function on \(U\). The function \(J\) is said to be: (i) strongly convex on \(U\) if there exists a constant \(r>0\) such that \[ \lambda J(u)+ (1- \lambda)J(v)- J(\lambda u+(1- \lambda)v)\geq r\lambda(1- \lambda)\| u- v\|^2 \] for all \(u,v\in U\), \(\lambda\in[0, 1]\); (ii) strongly quasiconvex on \(U\) if there exists a constant \(s>0\) such that \[ \max\{J(u), J(v)\}- J(\lambda u+(1- \lambda)v)\geq s\lambda(1- \lambda)\| u-v\|^2 \] for all \(u,v\in U\), \(\lambda\in[0, 1]\). The author asserts without proof that \(J\) is strongly convex (resp. strongly quasiconvex) on \(U\) if and only if the function \[ g(t)= J(v+ t/\| u- v\|(u- v)) \] is strongly convex (resp. strongly quasiconvex) on \([0,\| u-v\|]\) with the same constant for all \(u,v\in U\), \(u\neq v\). By applying this result it is shown that the Euclidean norm is strongly quasiconvex on any bounded convex subset of the space \(\mathbb{R}^n\).