relation: http://publicatio.bibl.u-szeged.hu/16252/ title: Dowker-type theorems for hyperconvex discs creator: Fejes Tóth Gábor creator: Fodor Ferenc description: A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of closed circular discs of radius r . A convex disc-polygon of radius r is a set with nonempty interior that is the intersection of a finite number of closed circular discs of radius r . We prove that the maximum area and perimeter of convex disc- n -gons of radius r contained in a hyperconvex disc of radius r are concave functions of n , and the minimum area and perimeter of disc- n -gons of radius r containing a hyperconvex disc of radius r are convex functions of n . We also consider hyperbolic and spherical versions of these statements. date: 2015 type: Folyóiratcikk type: PeerReviewed format: text identifier: http://publicatio.bibl.u-szeged.hu/16252/1/DOWKER-SZTEPubl.pdf identifier: Fejes Tóth Gábor; Fodor Ferenc: Dowker-type theorems for hyperconvex discs. PERIODICA MATHEMATICA HUNGARICA, 70 (2). pp. 131-144. ISSN 0031-5303 (2015) identifier: doi:10.1007/s10998-014-0071-y relation: http://real.mtak.hu/33619 relation: 2488534 language: eng