On the uniqueness of elements of the best approximation and the best one-sided approximation in the space $L_1$

Abstract

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 $(\alpha, \beta)$-approximation of continuous functions and the problem of the best one-sided approximation of continuously differentiable functions.