M. Pratsovytyi, Y. Goncharenko, I. Lysenko, S. Ratushniak
{"title":"Fractal functions of exponential type that is generated by the $\\mathbf{Q_2^*}$-representation of argument","authors":"M. Pratsovytyi, Y. Goncharenko, I. Lysenko, S. Ratushniak","doi":"10.30970/ms.56.2.133-143","DOIUrl":null,"url":null,"abstract":"We consider function $f$ which is depended on the parameters $0<a\\in R$, $q_{0n}\\in (0;1)$, $n\\in N$ and convergent positive series $v_1+v_2+...+v_n+...$, defined by equality $f(x=\\Delta^{Q_2^*}_{\\alpha_1\\alpha_2...\\alpha_n...})=a^{\\varphi(x)}$, where $\\alpha_n\\in \\{0,1\\}$, $\\varphi(x=\\Delta^{Q_2^*}_{\\alpha_1\\alpha_2...\\alpha_n...})=\\alpha_1v_1+...+\\alpha_nv_n+...$, $q_{1n}=1-q_{0n}$, $\\Delta^{Q_2^*}_{\\alpha_1...\\alpha_n...}=\\alpha_1q_{1-\\alpha_1,1}+\\sum\\limits_{n=2}^{\\infty}\\big(\\alpha_nq_{1-\\alpha_n,n}\\prod\\limits_{i=1}^{n-1}q_{\\alpha_i,i}\\big)$.In the paper we study structural, variational, integral, differential and fractal properties of the function $f$.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematychni Studii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/ms.56.2.133-143","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
We consider function $f$ which is depended on the parameters $0
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
