Geometry and nonlinear analysis in Banach spaces

Kondagunta Sundaresan

Vol. 102 (1982), No. 2, 487–498

DOI: 10.2140/pjm.1982.102.487

Abstract

It is proved that if a Banach space admits a nontrivial uniformly continuously differentiable function with bounded support then it is superreflexive. Several applications to approximation theory and existence of solutions to differential equations are discussed.

Mathematical Subject Classification 2000

Primary: 46B20

Secondary: 46G99, 58C20

Milestones

Received: 5 August 1980

Revised: 31 July 1981

Published: 1 October 1982