{"title":"费杰尔型算子对 H ⃗p η1,η2 类函数的近似分析","authors":"Yogeshkumar K. Patel, Rajendra G. Vyas","doi":"10.1515/gmj-2024-2041","DOIUrl":null,"url":null,"abstract":"In the present work, we explore Fejér-type operators within the mixed Lebesgue space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi>L</m:mi> <m:mover accent=\"true\"> <m:mi>p</m:mi> <m:mo stretchy=\"false\">→</m:mo> </m:mover> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo stretchy=\"false\">]</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2041_eq_0165.png\"/> <jats:tex-math>{L_{\\vec{p}}[\\mathbb{R}^{2}]}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and establish the degree of approximation for functions belonging to the class <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mi>H</m:mi> <m:mover accent=\"true\"> <m:mi>p</m:mi> <m:mo stretchy=\"false\">→</m:mo> </m:mover> <m:mrow> <m:msub> <m:mi>η</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>η</m:mi> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2041_eq_0161.png\"/> <jats:tex-math>{H_{\\vec{p}}^{\\eta_{1},\\eta_{2}}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> through the utilization of Fejér-type operators.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"49 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation of functions in H ⃗p η1,η2 class by Fejér-type operators\",\"authors\":\"Yogeshkumar K. Patel, Rajendra G. Vyas\",\"doi\":\"10.1515/gmj-2024-2041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present work, we explore Fejér-type operators within the mixed Lebesgue space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:msub> <m:mi>L</m:mi> <m:mover accent=\\\"true\\\"> <m:mi>p</m:mi> <m:mo stretchy=\\\"false\\\">→</m:mo> </m:mover> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\\\"false\\\">[</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo stretchy=\\\"false\\\">]</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2041_eq_0165.png\\\"/> <jats:tex-math>{L_{\\\\vec{p}}[\\\\mathbb{R}^{2}]}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and establish the degree of approximation for functions belonging to the class <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msubsup> <m:mi>H</m:mi> <m:mover accent=\\\"true\\\"> <m:mi>p</m:mi> <m:mo stretchy=\\\"false\\\">→</m:mo> </m:mover> <m:mrow> <m:msub> <m:mi>η</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>η</m:mi> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2041_eq_0161.png\\\"/> <jats:tex-math>{H_{\\\\vec{p}}^{\\\\eta_{1},\\\\eta_{2}}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> through the utilization of Fejér-type operators.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2024-2041\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2041","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本研究中,我们探讨了混合 Lebesgue 空间 L p → [ ℝ 2 ] {L_{\vec{p}}[\mathbb{R}^{2}]} 中的 Fejér 型算子,并通过利用 Fejér 型算子建立了属于 H p → η 1 , η 2 {H_{\vec{p}}^{\eta_{1},\eta_{2}}} 类函数的逼近度。
Approximation of functions in H ⃗p η1,η2 class by Fejér-type operators
In the present work, we explore Fejér-type operators within the mixed Lebesgue space Lp→[ℝ2]{L_{\vec{p}}[\mathbb{R}^{2}]} and establish the degree of approximation for functions belonging to the class Hp→η1,η2{H_{\vec{p}}^{\eta_{1},\eta_{2}}} through the utilization of Fejér-type operators.
期刊介绍:
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.