References
V. G.Boltianskii and P. S.Soltan, Combinatorial Geometry of Various Classes of Convex Sets. (Russian) Chişinău, Stiinţa 1978.
J. Borwein, A proof of the equivalence of Helly's and Krasnosel'skii's theorems. Canad. Math. Bull.20, 35–37 (1977).
M. Breen, A Krasnosel'skii-type theorem for points of local nonconvexity. Proc. Amer. Math. Soc.85, 261–266 (1982).
M. Breen, Krasnosel'skii-type theorems. In: Discrete Geometry and Convexity. Proc. Conf. New York 1982. Ann. New York Acad. Sci.440, 142–146 (1985).
M. Breen, Staircase kernels in orthogonal polygons. Arch. Math.59, 588–594 (1992).
H. Brunn, Über Kernelgebiete. Math. Ann.73, 436–440 (1913).
K. Kolodziejczyk, Starshapedness in convexity spaces. Compositio Math.56, 361–367 (1985).
K. Kolodziejczyk, The Starshapedness number and a Krasnosel'skii-type theorem in a convexity space. Arch. Math.49, 535–544 (1987).
M. A. Krasnosel'skii, Sur un critère pour qu'un domain soit étoilé. Mat. Sb.19, 309–310 (1946).
J. I.Munro, M.Overmars and D.Wood, Variations on visibility. In: Proc. Third Annu. Comput. Geom. ACM, Waterloo, Ontario Canada 1987.
M. Overmars andD. Wood, On rectangular visibility. J. Algorithms9, 372–390 (1988).
S. Schuierer, G. J. E. Rawlins andD. Wood, A generalization of staircase visibility. Lecture Notes in Comput. Sci.553, 277–287 (1991).
G.Sierksma, Axiomatic convexity theory and the convex product space. Doct. Diss. Univ. of Groningen, 1976.
P. S. Soltan, V. Garibi andV. Chepoi, Starshapedness in metric spaces and graphs. Proc. A. Vekua Inst. Appl. Math., Tbilissi University21, 31–48 (1990).
V. P. Soltan, Starshaped sets in the axiomatic theory of convexity. Bull. Acad. Sci. Georgian SSR96, 45–48 (1979).
V. P.Soltan, Introduction to Axiomatic Theory of Convexity. Chişinău, Stiinţa 1984.
O.Topală, Metric Starshapedness andL n -sets. Doct. Diss. University of Chişinău, 1980.
M.van de Vel, Theory of Convex Structures. Amsterdam 1993.
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Chepoi, V. On starshapedness in products of interval spaces. Arch. Math 64, 264–268 (1995). https://doi.org/10.1007/BF01188577
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DOI: https://doi.org/10.1007/BF01188577