{"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":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"486 ","pages":"Article 129072"},"PeriodicalIF":3.5000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324005332","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
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.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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