On Minkowski diagonal functions for two real numbers

Recently the authors proved that for irrationality measure functions $ψα(t),$ $ψβ(t),$ $α,β∈R$ the difference function $ψα(t)−ψβ(t)$ changes its sign infinitely many often as $t→∞,$ provided $α±β∉Z.$ In this paper we show that such a result is no longer true for Minkowski functions $μα(t),μβ(t).$ The result about oscillating of the difference $μα(t)−μβ(t)$ remains valid for almost all pairs (α,β).