Journal of Convex Analysis, Vol. 07, No. 2, pp. 319-334 (2000)

Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces

Butnariu, Dan; Iusem, Alfredo N.; Resmerita, Elena

Dept. of Mathematics University of Haifa 31905 Haifa Israel
Inst. de Matématica Pura e Aplicada Estrada Dońa Castorina 110 Rio de Janeiro, R.J., CEP 22460-320 Brazil
Dept. of Mathematics University of Haifa 31905 Haifa Israel

Abstract: The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first order Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.

Full text of the article:


[Previous Article] [Next Article] [Contents of this Number]
© 2003--2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition