Open Access Research

The Ptolemy constant of absolute normalized norms on ℝ2

Zhanfei Zuo

Author Affiliations

Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China

Journal of Inequalities and Applications 2012, 2012:107 doi:10.1186/1029-242X-2012-107

Published: 17 May 2012

Abstract

We determine and estimate the Ptolemy constant of absolute normalized norms on ℝ2 by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces.

2000 Mathematics Subject Classification: 46B20.

Keywords:
Ptolemy constant; absolute normalized norm; Lorentz sequence space; the Cesàro sequence space