Sandwich with periodicity

Hideaki Izumi, Lin Li, Janusz Matkowski, Małgorzta Wróbel

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Sandwich type results for p-sub-periodic, and p-super-periodic functions are presented. Given functions f, g: R→ R, we obtain necessary and sufficient conditions for the existence of a minimal p-periodic function F: R→ R and a maximal p-periodic function G: R→ R such that f(x) ≤ F(x) ≤ G(x) ≤ g(x). Moreover, the formulas for F and G are given, their semicontinuity, subadditivity and superadditivity as well as the lower semicontinuity of the set-valued function Φ(x):=[F(x),G(x)]are discussed. Finally, using Michael’s selection theorem, conditions ensuring the existence of a continuous p-periodic selection of the function Φ are also given.

Original languageEnglish
Pages (from-to)699-709
Number of pages11
JournalAequationes Mathematicae
Issue number4
Publication statusPublished - 2019 Aug 1
Externally publishedYes


  • Continuous selection
  • p-Periodic function
  • p-Sub-periodic
  • p-Super-periodic
  • Sandwich theorem
  • Semicontinuity

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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