On a generalisation of Local Uniform Rotundity

Uday Shankar Chakraborty ()
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Uday Shankar Chakraborty: Assam University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 439-448

Abstract: Abstract In this paper we investigate the property (HLUR), a generalisation of (LUR) property of a Banach space. A Banach space having the property (HLUR) is called an HLUR space. We characterise (HLUR) property with the help of known geometric properties and study various properties of HLUR spaces. We show that for any finite dimensional Banach space, the property (HLUR) coincides with anti-Daugavet property of the space. We also show some applications of HLUR spaces in connection with farthest points of sets.

Keywords: HLUR spaces; HS property; Locally uniformly rotund; Compactly locally uniformly rotund; Locally U-convex; Farthest point; Anti-Daugavet property; Primary 46B20; Secondary 41A65 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00062-3

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