Generalization of the concept of convexity in a hypercomplex space
DOI:
https://doi.org/10.26485/0459-6854/2018/68.2/9Keywords:
hypercomplexly convex set, h-hull of a set, h-extremal point, hextremal ray, H-quasiconvex set, linearly convex function, conjugate functionAbstract
Extremal elements and a h-hull of sets in the n-dimensional hypercomplex space Hn are investigated. The class of H-quasiconvex sets including strongly hypercomplexly convex sets and closed relatively to intersections is introduced. Some results concerning multivalued functions in the complex space were generalized into the n-dimensional hypercomplex space: there was proved the hypercomplex analogue of the Fenchel-Moreau theorem and some properties of functions that are conjugate to functions f : Hn \ Ɵ à H.
