A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes

Abstract

Abstract Let 𝓒 be a finite family of distinct boxes in ℝ d , let S = ⋃ {C : C in 𝓒} and let G be the intersection graph of 𝓒. For each block of G, assume that the corresponding members of 𝓒 have a staircase convex union. Then S with the rectilinear metric is a median space. Moreover, if every two points of S see a common point via staircase paths in S, then S is staircase starshaped.