There are some functions $$$T_y$$$, which are defined as:

• $$$\forall j\le 1,y\in (0,1):T_y(j):=1$$$
• $$$\forall y\in (0,1):T_y(x):=T_y(xy)+T_y(x-xy)+1$$$

Find $$$y$$$ (s) so that the order of $$$\lim_{x\rightarrow+\infty}T_y(x)$$$ is minimized.