The paper examines the functional transformation $K$ of the class $ORV_{\varphi}$ (see \cite{ex3}) into the class of positive functions on interval $(0,+ \infty)$ defined as follows: \begin{equation} K(f)=k_f, abel{eq:1} \end{equation} where \begin{equation*} k_f (ambda)= imsup_{x o +ıfty}\frac{f( ambda x)}{f(x)}, \quad ambda ı (0, + ıfty), \end{equation*} and $f \in ORV_{\varphi}$. Let $f \in IRV_{\varphi}$ or $SO_{\varphi}$ (see \cite{ex4}), $K$ be the transformation \eqref{eq:1} and for any $n \in \mathbb{N}$, $K_n(f)= \underbrace{ K(K\cdots(K}_\text{n}(f))\cdots),$ then the function $p(s)=\lim_{ n \to +\infty}K_n(f)(s)$, $s>0$, is $IRV_{\varphi}$ (and continuous) and $SO_{\varphi}$, respectively.