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On a generalisation of Local Uniform Rotundity

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  • Uday Shankar Chakraborty

    (Assam University)

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.

Suggested Citation

  • Uday Shankar Chakraborty, 2021. "On a generalisation of Local Uniform Rotundity," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 439-448, June.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00062-3
    DOI: 10.1007/s13226-021-00062-3
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