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For a complete totally ordered group (in the sense of [3], Ch. 14), let
, where
, with and ∗ extended from A to and, respectively
, in a natural way, and, for any set X, extend
, pointwise on X. For two sets X and W, we introduce and study
(by the conditions
and
for all
),which encompass various kinds of known conjugations and polarieis. We give some Applications to
, and to duality in optimization
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