L_p空间中非线性最佳逼近的广义强唯一性

Exteded Strong Uuicity of Nonlinear Best Approximation in L_p

本文讨论Lp（1＜P＜∞）中非线性最佳逼近的广义强唯一性·证明了定理：设G是Lp（1＜p＜∞）中闭集，如对有则G必为凸集．

This paper studies the extended strong nonlinear best approximation Lp,and Provesthe following theoremTheorem:Let G be a closed subset of Lp (l<P<∝),and if for every , the inequalityhold, in which q = max(2,p),then G is a Convex set.