On the uniqueness of elements of the best approximation and the best one-sided approximation in the space $L_1$ - Babenko, V. F.; Glushko, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
The problem of uniqueness of the best approximations in the space $L_1[a, b]$ is studied We consider the problem of the best approximation and the best $(α, β)$-approximation of continuous functions and the problem of the best one-sided approximation of continuously differentiable functions.