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A new approach with new solutions to the Matkowski and Wesołowski problem

descriptionPublicationkeyboard_double_arrow_right Article 22 Feb 2021 Poland English Publisher:Springer Science and Business Media LLCJournal:Aequationes mathematicae, volume 95, pages 761-776 (issn: 0001-9054, eissn: 1420-8903,

Authors: Janusz Morawiec; Thomas Zürcher;

doi: 10.1007/s00010-021-00788-9

handle: 20.500.12128/19453

A new approach with new solutions to the Matkowski and Wesołowski problem

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Abstract

AbstractBased on a result of de Rham, we give a family of functions solving the Matkowski and Wesołowski problem. This family consists of Hölder continuous functions, and it coincides with the whole family of solutions to the Matkowski and Wesołowski problem found earlier by a different method. Moreover, applying some results due to Hata and Yamaguti and due to Berg and Krüppel, we prove that there are functions solving the Matkowski and Wesołowski problem that are not Hölder continuous.

Country

Poland

Related Organizations

University of Silesia
Poland

Keywords

singular functions, Functional equations, Holder continuity

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