Best Simultaneous Approximation of Functions and a Generalized Minimax Theorem

TL;DR

This paper explores the best simultaneous approximation of functions using a generalized minimax theorem, providing new characterization and unicity results for approximations from finite-dimensional subspaces.

Contribution

It introduces a generalized minimax theorem to characterize and establish uniqueness of best simultaneous approximations in various norms.

Findings

Characterization theorems for BSA using a generalized minimax theorem

Strong unicity theorem for BSA from finite-dimensional subspaces

Applicable to finitely and infinitely many functions under uniform and other norms

Abstract

Best simultaneous approximation (BSA) for finitely or infinitely many functions are considered under the uniform norm and other important norms. Characterization theorems for a BSA from a finite-dimensional subspace are obtained by a generalized minimax theorem. From the characterization theorem a strong unicity theorem is also deduced for a BSA.