{"title":"lp,0的负定理","authors":"Ghazi Abdullah Madlol","doi":"10.31642/jokmc/2018/040301","DOIUrl":null,"url":null,"abstract":"For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: \n(2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p, \nwhere 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f Ì )〗_p is the degree of the best Lp approximation of the function f Ì by algebraic polynomial of degree not exceeding n.","PeriodicalId":115908,"journal":{"name":"Journal of Kufa for Mathematics and Computer","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"NEGATIVE THEOREM FOR LP,0\",\"authors\":\"Ghazi Abdullah Madlol\",\"doi\":\"10.31642/jokmc/2018/040301\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: \\n(2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p, \\nwhere 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f Ì )〗_p is the degree of the best Lp approximation of the function f Ì by algebraic polynomial of degree not exceeding n.\",\"PeriodicalId\":115908,\"journal\":{\"name\":\"Journal of Kufa for Mathematics and Computer\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Kufa for Mathematics and Computer\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31642/jokmc/2018/040301\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Kufa for Mathematics and Computer","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31642/jokmc/2018/040301","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship:
(2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p,
where 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f Ì )〗_p is the degree of the best Lp approximation of the function f Ì by algebraic polynomial of degree not exceeding n.