{"title":"Szasz-Mirakjan-Durrmeyer算子基于形状参数$\\lambda的逼近$","authors":"R. Aslan","doi":"10.31801/cfsuasmas.941919","DOIUrl":null,"url":null,"abstract":"In this\npaper, we study several approximation properties of\nSzasz-Mirakjan-Durrmeyer operators with shape parameter λ∈[−1,1]λ∈[−1,1]. Firstly, we obtain some preliminaries results such as moments and\ncentral moments. Next, we estimate\nthe order of convergence in terms of the usual modulus of continuity, for the\nfunctions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\\\\lambda$\",\"authors\":\"R. Aslan\",\"doi\":\"10.31801/cfsuasmas.941919\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this\\npaper, we study several approximation properties of\\nSzasz-Mirakjan-Durrmeyer operators with shape parameter λ∈[−1,1]λ∈[−1,1]. Firstly, we obtain some preliminaries results such as moments and\\ncentral moments. Next, we estimate\\nthe order of convergence in terms of the usual modulus of continuity, for the\\nfunctions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.\",\"PeriodicalId\":44692,\"journal\":{\"name\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31801/cfsuasmas.941919\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.941919","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$
In this
paper, we study several approximation properties of
Szasz-Mirakjan-Durrmeyer operators with shape parameter λ∈[−1,1]λ∈[−1,1]. Firstly, we obtain some preliminaries results such as moments and
central moments. Next, we estimate
the order of convergence in terms of the usual modulus of continuity, for the
functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.