Articles

On the Ratios of Arc Lengths to Chord Lengths in Real Banach Spaces

Published in: Quaestiones Mathematicae
Volume 33 , issue 3 , 2010 , pages: 347–367

DOI: 10.2989/16073606.2010.507326

Author(s): Senlin Wu Department of Mathematics, China , Chan He Department of Mathematics, China

Keywords: Arc length , chord length , uniform convexity , uniform nonsquareness , uniform normal structure

Abstract

Two new moduli are introduced to study the ratios of arc lengths to chord lengths in Banach spaces. Basic properties of those two moduli and the relation between them are studied. The relation between those two moduli and some geometric properties, including uniform convexity, uniform nonsquareness, and uniform normal structure, are discussed. Furthermore, some conditions implying fixed point property are presented.

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