We characterize the linear space ℋ of differences of support functions of convex bodies of 𝔼² and we consider every h ∈ ℋ as the support function of a generalized hedgehog (a rectifiable closed curve having exactly one oriented support line in each direction). The mixed area (for plane convex bodies identified with their support functions) has a symmetric bilinear extension to ℋ which can be interpreted as a mixed area for generalized hedgehogs. We study generalized hedgehogs and we extend the Minkowski inequality.
In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.
Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.
A multiobjective programming problem containing support functions is considered. Wolfe and Mond-Weir type vector duals to this problem are constructed and various duality results are validated under invexity and generalized invexity assumptions. Special cases are generated from these results.
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