The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight for continuous functions with values in KB-space

We investigate the problem of uniqueness of the best non-symmetrical $$$L_1$$$-approximant with a weight for continuous functions on metric compact set $$$Q$$$ with values in strictly convex partially ordered KB-space $$$X$$$ by subspaces of space $$$C(Q, X)$$$ of continuous functions on $$$Q$$$ with values in $$$X$$$. We obtain the characterization of subspaces of uniqueness of the best $$$(\alpha, \beta)$$$-approximant in integral metric with a weight for functions of space $$$C(Q, X)$$$ in terms of classes of "test" functions.