Proximinal and Cebysev Sets in Normed Linear Spaces

TL;DR

This paper investigates the conditions under which closed sets in normed linear spaces are proximinal or Chebyshev, contributing to the understanding of approximation theory in functional analysis.

Contribution

It provides new criteria for identifying proximinal and Chebyshev sets in normed linear spaces, advancing approximation theory.

Findings

Established conditions for proximinal sets

Derived criteria for Chebyshev sets

Enhanced understanding of approximation in normed spaces

Abstract

In this paper, we study a part of approximation theory that presents the conditions under which a closed set in a normed linear space is proximinal or Chebyshev.