{"title":"关于通过局部分数积分修正的辛普森式不等式","authors":"Abdelghani Lakhdari, Badreddine Meftah, Wedad Saleh","doi":"10.1515/gmj-2024-2030","DOIUrl":null,"url":null,"abstract":"The paper discusses corrected Simpson-type inequalities on fractal sets. Based on an introduced identity, we establish some error bounds for the considered formula using the generalized <jats:italic>s</jats:italic>-convexity and <jats:italic>s</jats:italic>-concavity of the local fractional derivative. Finally, we present some graphical representations justifying the established theoretical framework as well as some applications.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On corrected Simpson-type inequalities via local fractional integrals\",\"authors\":\"Abdelghani Lakhdari, Badreddine Meftah, Wedad Saleh\",\"doi\":\"10.1515/gmj-2024-2030\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper discusses corrected Simpson-type inequalities on fractal sets. Based on an introduced identity, we establish some error bounds for the considered formula using the generalized <jats:italic>s</jats:italic>-convexity and <jats:italic>s</jats:italic>-concavity of the local fractional derivative. Finally, we present some graphical representations justifying the established theoretical framework as well as some applications.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2024-2030\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2030","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文讨论了分形集上的修正辛普森式不等式。基于引入的特性,我们利用局部分形导数的广义 s 凸性和 s 凹性为所考虑的公式建立了一些误差边界。最后,我们给出了一些图形表示,证明了所建立的理论框架以及一些应用。
On corrected Simpson-type inequalities via local fractional integrals
The paper discusses corrected Simpson-type inequalities on fractal sets. Based on an introduced identity, we establish some error bounds for the considered formula using the generalized s-convexity and s-concavity of the local fractional derivative. Finally, we present some graphical representations justifying the established theoretical framework as well as some applications.
期刊介绍:
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.