CONTROLLING LIPSCHITZ FUNCTIONS

Andrey Kupavskii, János Pach, G. Tardos

Research output: Contribution to journalArticle

Abstract

Given any positive integers m and d, we say a sequence of points (x i ) i∈I in R m is Lipschitz-d-controlling if one can select suitable values yi (i ∈ I) such that for every Lipschitz function f :R m →R d there exists i with /f (x i ) - y i /<1. We conjecture that for every m = d, a sequence (x i ) i∈I ⊂ R m is d-controlling if and only if [Equation presented here] We prove that this condition is necessary and a slightly stronger one is already sufficient for the sequence to be d-controlling. We also prove the conjecture for m = 1.

Original languageEnglish
Pages (from-to)898-910
Number of pages13
JournalMathematika
Volume64
Issue number3
DOIs
Publication statusPublished - Jan 1 2018

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Lipschitz Function
Lipschitz
Sufficient
If and only if
Integer
Necessary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

CONTROLLING LIPSCHITZ FUNCTIONS. / Kupavskii, Andrey; Pach, János; Tardos, G.

In: Mathematika, Vol. 64, No. 3, 01.01.2018, p. 898-910.

Research output: Contribution to journalArticle

Kupavskii, Andrey ; Pach, János ; Tardos, G. / CONTROLLING LIPSCHITZ FUNCTIONS. In: Mathematika. 2018 ; Vol. 64, No. 3. pp. 898-910.
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