Geodesic
Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 319-334.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Mots-clés : Uniformly convex Banach space, totally convex function, duality mapping, Bregman projection 
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     author = {D. Butnariu and A. N. Iusem and E. Resmerita},
     title = {Total {Convexity} for {Powers} of the {Norm} in {Uniformly} {Convex} {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {319--334},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2000},
     url = {http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a4/}
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D. Butnariu; A. N. Iusem; E. Resmerita. Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces. Journal of convex analysis, Tome 7 (2000) no. 2, pp. 319-334. http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a4/