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

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.