Ultrametric preserving functions and weak similarities of ultrametric\n spaces

Let $WS(X, d)$ be the class of ultrametric spaces which are weakly similar to\nultrametric space $(X, d)$. The main results of the paper completely describe\nthe ultrametric spaces $(X, d)$ for which the equality $$ \\rho(x, y) =\nf(d(\\Phi(x), \\Phi(y))) $$ holds for every $(Y, \\rho) \\in WS(X, d)$, every weak\nsimilarity $\\Phi \\colon Y \\to X$, and all $x$, $y \\in Y$ with some ultrametric\n(pseudoultrametric) preserving function $f$ depending on $\\Phi$.\n