A Study on Optimal Approximation of Functional Subsets within Real Normed Spaces

Abstract

The optimal approximation of functional subsets within standard spaces facilitates data modeling and management of linear and nonlinear systems. In this paper, the best approximation in a real standard linear space X is described by the Kolmogorov theorem. In addition, the concepts of proximal set, smooth space, sun, sun point, and their relationship with the Kolmogorov condition are discussed. Finally, the effectiveness of using the best approximation in practical situations to achieve high accuracy in the computation of standard linear spaces is highlighted.