Strong Unicity of Restricted p-Centers

Abstract

Given a continuous seminorm p on a separated locally convex linear topological space X, we study in this paper strong uniqueness of the so-called restricted p-centers of sets. First we explore finite extremal characterizations of strongly unique restricted p-centers of subsets of X from its finite dimensional subspaces. Our main goal here is to investigate strong uniqueness of restricted p-centers of certain sets from the so-called p-RS sets, which are defined as closed convex sets that are obtained by imposing convex side constraints arising from boundedness of coefficients on translates of certain subspaces of X.

Keywords:

• p-RS sets
• Restricted p-centers
• Strict p-RS sets
• Strongly unique restricted p-centers

AMS Subject Classification:

• 41A28
• 41A65

ACKNOWLEDGMENTS

Thanks are due to Prof. C. Li for indicating to us that the proof of Theorem 4.3 of [23] is incomplete. Thanks are also due to a referee for his suggestion for inclusion of some of the older references pertaining to simultaneous approximation in a nonlinear setting.

This work was carried out during the tenure of the author as Emeritus Fellow of IIT Bombay.