Journal of Convex Analysis 28 (2021), No. 4, [final page numbers not yet available]
Copyright Heldermann Verlag 2021
Poidge-Convexity
Bo Wang
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, P. R. China
and: Hebei Key Laboratory of Computational Mathematics, Shijiazhuang, P. R. China
bow6666@163.com
Liping Yuan
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, P.R.China
and: Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, P.R.China
lpyuan@hebtu.edu.cn
Tudor Zamfirescu
Fachbereich Mathematik, Universität Dortmund, Germany, Germany
and: Roumanian Academy, Bucharest, Roumania, and: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, P.R.China
tuzamfirescu@gmail.com
We investigate in this paper the poidge-convexity, which is a generalization of right convexity, introduced by one of the present authors in 2014. Although not every convex body is poidge-convex, there are many families of compact sets, some of them very different from convex bodies, which are poidge-convex. We present here several such families.
Keywords: Poidge-convexity, starshaped sets, topological discs, polyhedral surfaces.
MSC: 52A01, 52A37.
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