Geodesic
Self Dual Operators on Convex Functionals; Geometric Mean and Square Root of Convex Functionals
Journal of convex analysis, Tome 8 (2001) no. 1, pp. 223-24

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

Let Conv(X) be the set of the convex functionals defined on a linear space X, with values in the union of R and the point of positive infinity. We give an extension of the notion of duality for (convex) functionals to mappings which operate from Conv(X) × Conv(X) into Conv(X). Afterwards, we present an algorithm which associates, under convenient assumptions, a self-dual operator to a given operator and its dual. Finally, we give some examples which prove the generality and interest of our approach. 
@article{JCA_2001_8_1_JCA_2001_8_1_a9,
     author = {M. Atteia and M. Ra{\"\i}ssouli},
     title = {Self {Dual} {Operators} on {Convex} {Functionals;} {Geometric} {Mean} and {Square} {Root} of {Convex} {Functionals}},
     journal = {Journal of convex analysis},
     pages = {223--24},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2001},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a9/}
}
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M. Atteia; M. Raïssouli. Self Dual Operators on Convex Functionals; Geometric Mean and Square Root of Convex Functionals. Journal of convex analysis, Tome 8 (2001) no. 1, pp. 223-24. http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a9/