# The convexity of Chebyshev sets in normed spaces

Document Type : Research Paper

Authors

1 Yazd University

2 Payame Noore Shiraz

Abstract

In this paper, we consider “Nearest points” and “Farthest points” in inner
product spaces and Hilbert spaces. The convexity of Chebyshev sets in Hilbert
spacse is an open problem. In this paper we define sun sets and sunrise sets in
normed spaces.

Keywords

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### History

• Receive Date: 07 July 2019
• Revise Date: 25 November 2020
• Accept Date: 04 May 2021
• First Publish Date: 04 May 2021