{"title":"西尔皮斯基垫圈上无边界点条件的 α 分形函数分析","authors":"Gurubachan , V.V.M.S. Chandramouli , S. Verma","doi":"10.1016/j.amc.2024.129072","DOIUrl":null,"url":null,"abstract":"<div><p>This note aims to manifest the existence of a class of <em>α</em>-fractal interpolation functions (<em>α</em>-FIFs) without boundary point conditions at the <em>m</em>-th level in the space consisting of continuous functions on the Sierpiński gasket (<em>SG</em>). Furthermore, we add the existence of the same class in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> space and energy space on <em>SG</em>. Under certain hypotheses, we show the existence of <em>α</em>-FIFs without boundary point conditions in the Hölder space and oscillation space on <em>SG</em>, and also calculate the fractal dimensions of their graphs.</p></div>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of α-fractal functions without boundary point conditions on the Sierpiński gasket\",\"authors\":\"Gurubachan , V.V.M.S. Chandramouli , S. Verma\",\"doi\":\"10.1016/j.amc.2024.129072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This note aims to manifest the existence of a class of <em>α</em>-fractal interpolation functions (<em>α</em>-FIFs) without boundary point conditions at the <em>m</em>-th level in the space consisting of continuous functions on the Sierpiński gasket (<em>SG</em>). Furthermore, we add the existence of the same class in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> space and energy space on <em>SG</em>. Under certain hypotheses, we show the existence of <em>α</em>-FIFs without boundary point conditions in the Hölder space and oscillation space on <em>SG</em>, and also calculate the fractal dimensions of their graphs.</p></div>\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324005332\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324005332","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Analysis of α-fractal functions without boundary point conditions on the Sierpiński gasket
This note aims to manifest the existence of a class of α-fractal interpolation functions (α-FIFs) without boundary point conditions at the m-th level in the space consisting of continuous functions on the Sierpiński gasket (SG). Furthermore, we add the existence of the same class in the space and energy space on SG. Under certain hypotheses, we show the existence of α-FIFs without boundary point conditions in the Hölder space and oscillation space on SG, and also calculate the fractal dimensions of their graphs.
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