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Archiv der Mathematik

, Volume 71, Issue 5, pp 399–406 | Cite as

Some properties of Gurarii's modulus of convexity

  • Luisa Sánchez
  • Antonio Ullán
Article

Abstract.

In 1967 Gurarii introduces a modulus of convexity, \(\beta _{E}(\varepsilon)\). In this paper some properties of this modulus are analyzed. They have their analogous on the well known- Clarkson's modulus of convexity, \(\delta _{E}(\varepsilon)\). In particular we show that \(\beta _{E}(\varepsilon)\) can be defined in several equivalent forms. We also prove that in lp spaces with 2 < p the Gurarii's modulus satifies the equality \(\beta _{l_p}(\varepsilon)=1-\root p \of{1-\left({\varepsilon} \over {2} \right)^p}\) for \(0\le \varepsilon \le 2\).

Keywords

Equivalent Form 

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Luisa Sánchez
    • 1
  • Antonio Ullán
    • 2
  1. 1.Departamento de Matemáticas, Universidad de los Andes, Mérida, VenezuelaVenezuela
  2. 2.Departamento de Matemáticas, Universidad de Extremadura, E-06071 Badajoz, SpainSpain

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