{"paper":{"title":"On a problem of Janusz Matkowski and Jacek Weso{\\l}owski","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Janusz Morawiec, Thomas Z\\\"urcher","submitted_at":"2017-03-24T15:24:35Z","abstract_excerpt":"We study the problem of the existence of increasing and continuous solutions $\\varphi\\colon[0,1]\\to[0,1]$ such that $\\varphi(0)=0$ and $\\varphi(1)=1$ of the functional equation \\begin{equation*} \\varphi(x)=\\sum_{n=0}^{N}\\varphi(f_n(x))-\\sum_{n=1}^{N}\\varphi(f_n(0)), \\end{equation*} where $N\\in\\mathbb N$ and $f_0,\\ldots,f_N\\colon[0,1]\\to[0,1]$ are strictly increasing contractions satisfying the following condition $0=f_0(0)<f_0(1)=f_1(0)<\\cdots<f_{N-1}(1)=f_N(0)<f_N(1)=1$. In particular, we give an answer to the problem posed in the article Remark on BV-solutions of a functional equation connec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08459","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}