【摘要】 本文从Banach空间几何学在逼近论中应用的视角,结合作者所做的一些工作,对最佳逼近问题中最佳逼近元的存在性、几乎存在性、最佳逼近问题的适定性及度量投影算子的连续性四方面问题近年来的研究进展作了系统介绍和综述,并提出一些开问题.更多还原

【Abstract】 From the perspective of the application of Banach space geometry in approximation theory,combined with some work done by the author,the paper systematically introduces and summarizes the research progress of the following four aspects—the existence and almost existence of the best approximation element,the well-posedness of the best approximation problem and the continuity of the metric projection operator in recent years.Some open problems are also put forward in this paper.更多还原