On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces

For arbitrary $(q_1,q_2)$-quasimetric space, it is proved that there exists a function $f,$ such that $f$-triangle inequality is more exact than any $(q_1,q_2)$-triangle inequality. It is shown that this function $f$ is the least one in the set of all concave continuous functions $g$ for which $g$-triangle inequality hold.