On a problem of Janusz Matkowski and Jacek Wesołowski

2017/03/24 by Janusz Morawiec, Morawiec, Janusz, Thomas Zürcher +1
Mathematics · #26A46 #28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #Primary 39B12 #Secondary 26A30

paper · pdf · doi:10.48550/arxiv.1703.08459

openalex publication_date 2017/03/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We study the problem of the existence of increasing and continuous solutions φ\colon[0,1]→[0,1] such that φ(0)=0 and φ(1)=1 of the functional equation φ(x)=∑_n=0^Nφ(f_n(x))-∑_n=1^Nφ(f_n(0)), where N∈\mathbb N and f₀,…,f_N\colon[0,1]→[0,1] are strictly increasing contractions satisfying the following condition 0=f₀(0)

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