W. Alshanti, I. Batiha, Ahmad Alshanty, A. Zraiqat, I. Jebril, Ma’mon Ahmad Abu
{"title":"扰动类梯形不等式","authors":"W. Alshanti, I. Batiha, Ahmad Alshanty, A. Zraiqat, I. Jebril, Ma’mon Ahmad Abu","doi":"10.26554/sti.2023.8.2.205-211","DOIUrl":null,"url":null,"abstract":"In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.","PeriodicalId":21644,"journal":{"name":"Science and Technology Indonesia","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Perturbed Trapezoid Like Inequalities\",\"authors\":\"W. Alshanti, I. Batiha, Ahmad Alshanty, A. Zraiqat, I. Jebril, Ma’mon Ahmad Abu\",\"doi\":\"10.26554/sti.2023.8.2.205-211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.\",\"PeriodicalId\":21644,\"journal\":{\"name\":\"Science and Technology Indonesia\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science and Technology Indonesia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26554/sti.2023.8.2.205-211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Pharmacology, Toxicology and Pharmaceutics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science and Technology Indonesia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26554/sti.2023.8.2.205-211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Pharmacology, Toxicology and Pharmaceutics","Score":null,"Total":0}
In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.
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