A Krasnosel'skii theorem for orthogonal polygons starshaped via staircase (n+1)-paths

作者：Breen Marilyn^*

来源：Aequationes Mathematicae, 2010, 79(1-2): 99-110.

DOI：10.1007/s00010-010-0010-9

• Orthogonal polygons
• sets starshaped via staircase (n+1)-paths

Let S be a simply connected orthogonal polygon in the plane, and let n be fixed, n >= 1. If every two points of S are visible via staircase n-paths from a common point of S, then S is starshaped via staircase (n + 1)-paths. Moreover, the associated staircase (n + 1)kernel is staircase (n + 1)-convex. The number two is best possible, and the number n + 1 is best possible for n >= 2.

• 出版日期2010-3