Conjecture on the Steiner diameter and Steiner (k,k')-radius of trees

Let $n$, $k$, and $k^{\prime}$ be integers with $n\geq k\geq3$ and $k>k^{\prime}\geq1$, and let $T$ be a tree with order $n$. The Steiner diameter–radius conjecture.

$$Sd_k(T)\leq\frac{k}{k-k^{\prime}}Sr_{k,k^{\prime}}(T)-\frac{k^{\prime}(k^{\prime}-1)}{k-k^{\prime}}.$$

The paper proves the inequality for $k^{\prime}=2$ and $k^{\prime}=3$, and states that it generalizes the known result for $k^{\prime}=1$. Its validity for all $k^{\prime}\geq1$ under the displayed hypotheses remains open.