A Study of Operators in Approximation Theory

摘要

This dissertation consists of two independent chapters. The first chapter studies constants associated with best-approximation maps mainly in the space of all real-valued continuous functions on a closed interval. The second chapter contains several generalizations of a theorem due to Cheney and Goldstein. This theorem establishes the existence of bounded linear operators which best approximate nonlinear operators under certain conditions. The well-known Alaoglu theorem is also obtained in this chapter as a special case of more general theorems. (Author)