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On a problem of Janusz Matkowski and Jacek Wesołowski
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Morawiec, Janusz and Zürcher, Thomas (2018) On a problem of Janusz Matkowski and Jacek Wesołowski. Aequationes Mathematicae, 92 . pp. 601-615. doi:10.1007/s00010-018-0556-5 ISSN 0001-9054.
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Official URL: https://doi.org/10.1007/s00010-018-0556-5
Abstract
We study the problem of the existence of increasing and continuous solutions φ :[0 , 1] → [0 , 1] such that φ (0) = 0 and φ (1) = 1 of the functional equation
φ ( x )= N ∑ n =0 φ ( f n ( x )) − N ∑ n =1 φ ( f n (0)) ,
where N ∈ N and f 0 ,...,f N :[0 , 1] → [0 , 1] are strictly increasing contractions satisfying the following condition 0 = f 0 (0) <f 0 (1) = f 1 (0) < ··· <f N − 1 (1) = f N (0) <f N (1) = 1. In particular, we give an answer to the problem posed in Matkowski (Aequationes Math. 29:210–213, 1985 ) by Janusz Matkowski concerning a very special case of that equation.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Functional equations, Functions, Continuous | ||||||||||||
Journal or Publication Title: | Aequationes Mathematicae | ||||||||||||
Publisher: | Springer | ||||||||||||
ISSN: | 0001-9054 | ||||||||||||
Official Date: | August 2018 | ||||||||||||
Dates: |
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Volume: | 92 | ||||||||||||
Page Range: | pp. 601-615 | ||||||||||||
DOI: | 10.1007/s00010-018-0556-5 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 10 May 2018 | ||||||||||||
Date of first compliant Open Access: | 10 May 2018 | ||||||||||||
RIOXX Funder/Project Grant: |
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