{"title":"Generalized results of Majorization inequality via Lidstone's polynomial and newly Green function","authors":"N. Latif, J. Pečarić, N. Siddique","doi":"10.22436/jnsa.011.06.08","DOIUrl":null,"url":null,"abstract":"Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pecari ˇ c, J. Inequal. Appl., ´ 2017 (2017), 17 pages] and Lidstone’s polynomial. We find new upper bounds of Gruss and Ostrowski type. We give further results of majorization inequality by making linear functionals constructed on ¨ convex functions. Some applications are given.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"50 1","pages":"812-831"},"PeriodicalIF":0.0000,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jnsa.011.06.08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pecari ˇ c, J. Inequal. Appl., ´ 2017 (2017), 17 pages] and Lidstone’s polynomial. We find new upper bounds of Gruss and Ostrowski type. We give further results of majorization inequality by making linear functionals constructed on ¨ convex functions. Some applications are given.
利用[N]中定义的新Green函数，得到了多数化不等式的推广结果。马茂德，r.p. Agarwal, S. I. Butt, J. Pecari, c, J.不等式。达成。， ' 2017(2017)， 17页]和Lidstone的多项式。我们找到了新的Gruss型和Ostrowski型的上界。通过构造在凸函数上构造的线性泛函，给出了多数化不等式的进一步结果。给出了一些应用。
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