Total convexity for powers of the norm in uniformly convex Banach spaces

Citation
D. Butnariu et al., Total convexity for powers of the norm in uniformly convex Banach spaces, J CONVEX AN, 7(2), 2000, pp. 319-334
Citations number
25
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF CONVEX ANALYSIS
ISSN journal
09446532 → ACNP
Volume
7
Issue
2
Year of publication
2000
Pages
319 - 334
Database
ISI
SICI code
0944-6532(2000)7:2<319:TCFPOT>2.0.ZU;2-C
Abstract
We show that in any uniformly convex Banach space the functions f(x) = \ \x \ \ (r) with r is an element of (1, infinity) are totally convex. Using th is fact we establish a formula for determining Bregman projections on close d hyperplanes and half spaces. This leads to a method for solving linear op erator equations (e.g., first kind Fredholm and Volterra equations) in spac es which are uniformly convex and smooth.