The aim of this paper is the investigation of weakly H-quasiconvex functions in the framework of the Heisenberg group ℍ. The functions of this class, recently introduced by Sun and Yang, are defined via the property that their subleveis are weakly H-convex subsets of ℍ. Following Crouzeix's approach, we prove conditions of first and second order, easily testable, for regular weakly H-quasiconvex functions, and we provide a characterization of them. © Heldermann Verlag.
Calogero, A., Carcano, G., Pini, R. (2008). On weakly H-quasiconvex functions on the heisenberg group. JOURNAL OF CONVEX ANALYSIS, 15(4), 753-766.
On weakly H-quasiconvex functions on the heisenberg group
CALOGERO, ANDREA GIOVANNI;CARCANO, GIOVANNA;PINI, RITA
2008
Abstract
The aim of this paper is the investigation of weakly H-quasiconvex functions in the framework of the Heisenberg group ℍ. The functions of this class, recently introduced by Sun and Yang, are defined via the property that their subleveis are weakly H-convex subsets of ℍ. Following Crouzeix's approach, we prove conditions of first and second order, easily testable, for regular weakly H-quasiconvex functions, and we provide a characterization of them. © Heldermann Verlag.
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