局部凸空间和赋范空间上的最佳共逼近

BEST COAPPROXIMATION IN LOCALLY CONVEX SPACES AND NORMED LINEAR SPACES

研究了局部凸空间和赋范线性空间中的 (f_)共逼近和强 (f_)共逼近的一些性质 ,给出了f_共逼近、强f_共逼近和强f_Kolmogorov集的特征定理 ;并举例说明RaoGS的两主要定理是不正确的 ,同时作了相应的更正 .所得结果中的部分推广和改进了SongWenhua ,RaoGS和NarangTD等人的相应结果 .

Some properties of (f-) coapproximation and strongly (f-) coapproximation are studied in locally convex spaces and normed linear spaces. The characterization theorems of f-coapproximation, strongly f-coapproximation and Strongly f-Kolmogorov set in locally convex spaces are obtained. Meanwhile, two examples are given to show that two (main) theorems of Rao G S do not hold, and the corresponding correction is presented parts of our results are extension and improvement of the corresponding results from Song Wenhua, Rao G S, Narang T D,et al.