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.

Author information

Contact details are reproduced from the original publication and may be historical.

Dan Butnariu

Dept. of Mathematics, University of Haifa, 31905 Haifa, Israel

Alfredo N. Iusem

Inst. de Matemática Pura e Aplicada, Estrada Doña Castorina 110, Rio de Janeiro, R.J., CEP 22460-320, Brazil

Elena Resmerita

Dept. of Mathematics, University of Haifa, 31905 Haifa, Israel

Keywords

  • Uniformly convex Banach space
  • totally convex function
  • duality mapping
  • Bregman projection

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Suggested citation

D. Butnariu, A. N. Iusem, E. Resmerita. “Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces.” Journal of Convex Analysis 7 (2000), No. 2, 319–334. https://doi.org/10.68381/jca07016

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Published by Heldermann Verlag, 2000. Rights now held by Banach Press.