V -dualities and ⊥-dualities
Juan Enrique Martínez-Legaz, Ivan Singer · Optimization · 1991
We introduce and study dualities △:[Rbar]x → [Rbar]w (i.e., mappings f ε [Rbar]x → f △ ε [Rbar]w such that for all {fi }iε1 ∈ Rx and all index sets I), which satisfy the additional condition and their duals, which are characterized as those dualities △*:Rx → Rw for which , where ⊥ and ⊺ are two new binary operations on [Rbar], which we introduce here. Furthermore, we give a characterization of those Δ which are also conjugations. Some applications are also mentioned.