Let X be a non-empty set. A symmetric function is called an ultra function on X if for all x,y,z. If G is a subset of a set X with an ultra function f then an element is said to be (i) an f-best approximation to if for all and (ii) an f- best coapproximation to x if for all . In this paper we extend some of the known results on best approximation and best coapproximation in non-Archimedean normed linear spaces to approximation relative to an ultra function which is defined either on an arbitrary set X or on a Hausdorff topological vector space X over a non- Archimedean valued field F.
|41A50||Best approximation, Chebyshev systems|