Banach空间中非线性最佳逼近的广义强唯一性

GENERALIZED STRONG UNICITY OF NONLINEAR BEST APPROXIMATION IN BANACH SPACES

设X是一致凸空间，G为X中太阳集，R．Smarzewski[1]证明了g∈G对x∈的最佳逼近具有广义强唯一性，本文讨论其逆，在最佳逼近是广义强唯一的条件下，研究了空间的凸性和逼近集的太阳性．

Let X be a uniformly convex space, G a sunset of X. R.Smarzewski[1] proved that a best approximation g∈ G to element x∈ X must have the generalized strong unicity.In this paper,we study the inverse problem, that is, under the condition that the best approximation is a generalized strongly unique best approximation, we study the convexity of spaces and the solar properties of approximation sets.