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 Cet article a éte moissonné depuis la source Heldermann Verlag

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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},
     year = {2000},
     volume = {7},
     number = {2},
     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/