GENERALIZED STRONG UNICITY OF NONLINEAR BEST APPROXIMATION IN BANACH SPACES
Banach 空间中非线性最佳逼近的广义强唯一性

Let X be a uniformly convex space, G a sunset of X. R.Smarzewski proved that a best approximation g implied by G to element x implied by 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.