A look at proximinal and Chebyshev sets in Banach spaces

Abstract

The main aim of this survey is to present some classical as well asrecent characterizations involving the notion of proximinal and Chebyshev sets inBanach spaces. In particular, we discuss the convexity of Chebyshev sets.

Keywords

• Approximatively compact
• Proximinality
• Chebyshevity
• Minimizing sequence.