{"title":"分形连续函数盒维估计的若干结果","authors":"HUAI YANG, LULU REN, QIAN ZHENG","doi":"10.1142/s0218348x24500506","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we explore upper box dimension of continuous functions on <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">]</mo></math></span><span></span> and their Riemann–Liouville fractional integral. Firstly, by comparing function limits, we prove that the upper box dimension of the Riemann–Liouville fractional order integral image of a continuous function will not exceed <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn><mo stretchy=\"false\">−</mo><mi>υ</mi></math></span><span></span>, the result similar to [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, <i>Acta Math. Appl. Sin. E</i><b>32</b> (2016) 1494–1508]. Secondly, we prove that upper box dimension of multiple algebraic sums of continuous functions does not exceed the largest box dimension among them, backing up our conclusion with an appropriate example. Finally, we draw the same conclusions for the product of multiple continuous functions.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SOME RESULTS ON BOX DIMENSION ESTIMATION OF FRACTAL CONTINUOUS FUNCTIONS\",\"authors\":\"HUAI YANG, LULU REN, QIAN ZHENG\",\"doi\":\"10.1142/s0218348x24500506\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we explore upper box dimension of continuous functions on <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mo stretchy=\\\"false\\\">[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\\\"false\\\">]</mo></math></span><span></span> and their Riemann–Liouville fractional integral. Firstly, by comparing function limits, we prove that the upper box dimension of the Riemann–Liouville fractional order integral image of a continuous function will not exceed <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mn>2</mn><mo stretchy=\\\"false\\\">−</mo><mi>υ</mi></math></span><span></span>, the result similar to [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, <i>Acta Math. Appl. Sin. E</i><b>32</b> (2016) 1494–1508]. Secondly, we prove that upper box dimension of multiple algebraic sums of continuous functions does not exceed the largest box dimension among them, backing up our conclusion with an appropriate example. Finally, we draw the same conclusions for the product of multiple continuous functions.</p>\",\"PeriodicalId\":501262,\"journal\":{\"name\":\"Fractals\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractals\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218348x24500506\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218348x24500506","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文探讨了[0,1]上连续函数的上盒维及其黎曼-黎奥维尔分阶积分。首先，通过比较函数极限，我们证明了连续函数的黎曼-黎奥维尔分数阶积分图像的上盒维不会超过 2-υ，这一结果与 [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral image of a continuous function] 类似。S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous function, Acta Math.Appl.E32 (2016) 1494-1508].其次，我们证明连续函数的多个代数和的上盒维不超过其中最大的盒维，并用一个适当的例子来支持我们的结论。最后，我们对多个连续函数的乘积得出了同样的结论。
SOME RESULTS ON BOX DIMENSION ESTIMATION OF FRACTAL CONTINUOUS FUNCTIONS
In this paper, we explore upper box dimension of continuous functions on and their Riemann–Liouville fractional integral. Firstly, by comparing function limits, we prove that the upper box dimension of the Riemann–Liouville fractional order integral image of a continuous function will not exceed , the result similar to [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, Acta Math. Appl. Sin. E32 (2016) 1494–1508]. Secondly, we prove that upper box dimension of multiple algebraic sums of continuous functions does not exceed the largest box dimension among them, backing up our conclusion with an appropriate example. Finally, we draw the same conclusions for the product of multiple continuous functions.
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