On the calculation of the Dunkl-Williams constant of normed linear spaces

• DOI: 10.2478/s11533-013-0238-4
• Publication Date: 2013-04-30T20:18:06Z
• Authors: Hiroyasu Mizuguchi; Kichi-Suke Saito; Ryotaro Tanaka
• Keywords: Convexity; Constant (computer programming); Smoothness; Linear space; Reflexive space

Abstract Recently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the constant DW(X) of a normed linear space X. In this paper we present some characterizations constant. As an application, calculate DW(ℓ2-ℓ∞) in Day-James ℓ2-ℓ∞.