On Smooth Variational Principles in Banach Spaces

A new smooth variational principle for spaces admitting Fr´echet differentiable bump functions is proved. Further it is shown that each proper lower semicontinuous bounded below function can be supported by a smooth function with locally H¨older derivative if and only if the space is superreflexive. Some geometrical refinements of the Borwein]Preiss smooth variational principle using Deville’s techniques are obtained. Q 1996 Academic Press, Inc.