Journal of convex analysis, Tome 8 (2001) no. 1, pp. 223-24
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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/
@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},
year = {2001},
volume = {8},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a9/}
}
TY - JOUR
AU - M. Atteia
AU - M. Raïssouli
TI - Self Dual Operators on Convex Functionals; Geometric Mean and Square Root of Convex Functionals
JO - Journal of convex analysis
PY - 2001
SP - 223
EP - 24
VL - 8
IS - 1
UR - http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a9/
ID - JCA_2001_8_1_JCA_2001_8_1_a9
ER -
%0 Journal Article
%A M. Atteia
%A M. Raïssouli
%T Self Dual Operators on Convex Functionals; Geometric Mean and Square Root of Convex Functionals
%J Journal of convex analysis
%D 2001
%P 223-24
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a9/
%F JCA_2001_8_1_JCA_2001_8_1_a9
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.
