Abstract
We prove a generalization of the Krasnosel’ski theorem on star-shaped sets. Usingd-segments inn-dimensional Minkowski spaces instead of usual segments, the notions “d-visibility” and “d-star-shapedness” are introduced. Our main aim is to give necessary and sufficient conditions ford-star-shapedness in finite-dimensional normed spaces.
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Boltyanski, V., Martini, H. & Soltan, P.S. Star-shaped sets in normed spaces. Discrete Comput Geom 15, 63–71 (1996). https://doi.org/10.1007/BF02716579
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DOI: https://doi.org/10.1007/BF02716579