Singleton Relative Chebyshev Center in Best Simultaneous Approximations

摘要

This report will conclude an extensive study of the relative Chebyshev center and best simultaneous approximation theory. The author considers the current concept of the Chebyshev center as developed by Garkavi, and examines in depth the relative Chebyshev center and concentrates on the special circumstances when the relative Chebyshev center reduces to a single point (singleton set). While the notations and definitions of the relative Chebyshev center and the best simultaneous approximation of elements are different, the ultimate aim and the general concept are the same. Since the field is relatively new, there doesn't appear to be any standardization among the contemporary literature concerning terminology or notation. Thus the relative Chebyshev center is shown to be a singleton, we have the unique element or best simultaneous approximation. The intent is to give a sampling of the major work that has been done in this field so far. But first, let us describe in a more elementary way, the basic idea behind the relative Chebyshev center. Keywords: Normed linear space.