We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin … other duality operators of convex objects. …

This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and …-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality … in the paper. Basic properties of the extended duality, including the extended bi-polar theorem, are proven. Examples are …

to the development of the duality formulas of convex calculus. This is done by means of one single method: firstly conify … definitions of convex objects, duality operators, binary operations and duality formulas, all without the usual need to exclude … degenerate situations. The duality operator for convex function agrees with the usual one, the Legendre-Fenchel transform, only …

This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and …-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality … cones and are convenient to use for some practical applications. Properties of the extended duality, including the extended …