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

Abstract

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.

Keywords

• uniqueness of the best non-symmetric approximant with a weight
• $(\alpha
• \beta)$-approximation with a weight
• integral metric
• KB-space