半实轴上的非线性最佳逼近

Approximation by Nonlinear Families on [0, +∞]

中文摘要:

      设h(x)为严格下降于零的连续函数.并且h(0)=1.设f、g∈C[0,+∞),定义距离为d(f,g)=(?)(x)(|f(x)-g(x)|)/(1+|f(x)-g(x)|).本文在这个距离空间中引进了D中间性集和弱D中间性集的概念,并且考虑了在这两类集上的最佳逼近问题,建立了最佳逼近元的一些特征刻划.

英文摘要:

      Let C[0,+∞) be the space of continuous functions on [0, +∞). For f,g ∈C[0,+∞), their distance is defined by d(f,g)=(?)(x)(|f(x)-g(x)|)/(1+|f(x)-g(x)|), where h(x) is a strictly decreasing continuous function and h(0, 1), (?)h(x)=0.Here, we consider approximation by the familieэ with the D betweeness property or the weak D betweeness propert. The characterzations of best approximation are studied.