M. Pratsovytyi, Y. Goncharenko, I. Lysenko, S. Ratushniak
{"title":"由参数的$\\mathbf{Q_2^*}$-表示生成的指数型分形函数","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":"{\"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}","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}
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