{"title":"分数阶Cesàro矩阵及其相关序列空间","authors":"H. Roopaei, M. İlkhan","doi":"10.1515/conop-2020-0112","DOIUrl":null,"url":null,"abstract":"Abstract In this research, we introduce a new fractional Cesàro matrix and investigate the topological properties of the sequence space associated with this matrix.We also introduce a fractional Gamma matrix aswell and obtain some factorizations for the Hilbert operator based on Cesàro and Gamma matrices. The results of these factorizations are two new inequalities one ofwhich is a generalized version of thewell-known Hilbert’s inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"8 1","pages":"24 - 39"},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2020-0112","citationCount":"3","resultStr":"{\"title\":\"Fractional Cesàro Matrix and its Associated Sequence Space\",\"authors\":\"H. Roopaei, M. İlkhan\",\"doi\":\"10.1515/conop-2020-0112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this research, we introduce a new fractional Cesàro matrix and investigate the topological properties of the sequence space associated with this matrix.We also introduce a fractional Gamma matrix aswell and obtain some factorizations for the Hilbert operator based on Cesàro and Gamma matrices. The results of these factorizations are two new inequalities one ofwhich is a generalized version of thewell-known Hilbert’s inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.\",\"PeriodicalId\":53800,\"journal\":{\"name\":\"Concrete Operators\",\"volume\":\"8 1\",\"pages\":\"24 - 39\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/conop-2020-0112\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Concrete Operators\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/conop-2020-0112\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2020-0112","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Fractional Cesàro Matrix and its Associated Sequence Space
Abstract In this research, we introduce a new fractional Cesàro matrix and investigate the topological properties of the sequence space associated with this matrix.We also introduce a fractional Gamma matrix aswell and obtain some factorizations for the Hilbert operator based on Cesàro and Gamma matrices. The results of these factorizations are two new inequalities one ofwhich is a generalized version of thewell-known Hilbert’s inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.
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