Minkowski sums of Cantor-type sets

Volume 119 / 2010

Kazimierz Nikodem, Zsolt Páles Colloquium Mathematicum 119 (2010), 95-108 MSC: Primary 28A80; Secondary 52A37, 39B62. DOI: 10.4064/cm119-1-5


The classical Steinhaus theorem on the Minkowski sum of the Cantor set is generalized to a large class of fractals determined by Hutchinson-type operators. Numerous examples illustrating the results obtained and an application to $t$-convex functions are presented.


  • Kazimierz NikodemDepartment of Mathematics and Computer Science
    University of Bielsko-Biała
    Willowa 2
    43-309 Bielsko-Biała, Poland
  • Zsolt PálesInstitute of Mathematics
    University of Debrecen
    H-4010 Debrecen, Pf. 12, Hungary

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