{"title":"某些组成算子的收敛估计","authors":"Vijay Gupta","doi":"10.33205/cma.1474535","DOIUrl":null,"url":null,"abstract":"There are different methods available in literature to construct a new operator. One of the methods to construct an operator is the composition method. It is known that Baskakov operators can be achieved by composition of Post Widder $P_n$ and Sz\\'asz-Mirakjan $S_n$ operators in that order, which is a discretely defined operator. But when we consider different order composition namely $S_n\\circ P_n$, we get another different operator. Here we study such and we establish some convergence estimates for the composition operators $S_n\\circ P_n$, along with difference with other operators. Finally we found the difference between two compositions by considering numeric values.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence estimates for some composition operators\",\"authors\":\"Vijay Gupta\",\"doi\":\"10.33205/cma.1474535\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"There are different methods available in literature to construct a new operator. One of the methods to construct an operator is the composition method. It is known that Baskakov operators can be achieved by composition of Post Widder $P_n$ and Sz\\\\'asz-Mirakjan $S_n$ operators in that order, which is a discretely defined operator. But when we consider different order composition namely $S_n\\\\circ P_n$, we get another different operator. Here we study such and we establish some convergence estimates for the composition operators $S_n\\\\circ P_n$, along with difference with other operators. Finally we found the difference between two compositions by considering numeric values.\",\"PeriodicalId\":36038,\"journal\":{\"name\":\"Constructive Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Constructive Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33205/cma.1474535\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33205/cma.1474535","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Convergence estimates for some composition operators
There are different methods available in literature to construct a new operator. One of the methods to construct an operator is the composition method. It is known that Baskakov operators can be achieved by composition of Post Widder $P_n$ and Sz\'asz-Mirakjan $S_n$ operators in that order, which is a discretely defined operator. But when we consider different order composition namely $S_n\circ P_n$, we get another different operator. Here we study such and we establish some convergence estimates for the composition operators $S_n\circ P_n$, along with difference with other operators. Finally we found the difference between two compositions by considering numeric values.