Hardy-Littlewood-Polya relation in the best dominated approximation in symmetric spaces

JOURNAL OF APPROXIMATION THEORY

卷:213

Article

Ciesielski, Maciej¹ 

[1] Poznan Univ Tech, Inst Math, Piotrowo 3A, PL-60965 Poznan, Poland

关键词: Symmetric space;    Strict K-monotonicity;    K-order continuity;    The best approximant;   

DOI  :  10.1016/j.jat.2016.10.001

来源: Elsevier

【 摘 要 】

We investigate a correspondence between strict K-monotonicity, K-order continuity and the best dominated approximation problems with respect to the Hardy-Littlewood-Polya relation <. Namely, we study, in terms of an LKM point and a UKM point, a necessary condition for uniqueness of the best dominated approximation under the relation < in a symmetric space E. Next, we characterize a relation between a point of K-order continuity and an existence of a best dominated approximant with respect to < Finally, we present a compete criteria, written in a notion of K-order continuity, under which a closed and K-bounded above subset of a symmetric space E is proximinal. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free