{"title":"与积分算子相关的亚纯函数的一些性质","authors":"W. Y. Kota, R. M. El-Ashwah","doi":"10.1186/s42787-023-00163-4","DOIUrl":null,"url":null,"abstract":"Abstract In the present paper we aim at proving some subordinations properties for meromorphic functions analytic in the punctured unit disc $$\\Delta ^*=\\{z:0<|z|<1\\}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>Δ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>z</mml:mi> <mml:mo>:</mml:mo> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mo>|</mml:mo> <mml:mi>z</mml:mi> <mml:mo>|</mml:mo> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> with a simple pole at the origin. The functions under investigation are associated with two integral operators $$\\mathcal {P}_\\sigma ^\\gamma$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>P</mml:mi> <mml:mi>σ</mml:mi> <mml:mi>γ</mml:mi> </mml:msubsup> </mml:math> and $$\\mathcal {Q}_\\sigma ^\\gamma$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>Q</mml:mi> <mml:mi>σ</mml:mi> <mml:mi>γ</mml:mi> </mml:msubsup> </mml:math> (see Lashin in Comput Math Appl 59:524–531, 2010, https://doi.org/10.1016/j.camwa.2009.06.015 ). Several other results and numerical examples are also obtained.","PeriodicalId":33345,"journal":{"name":"Journal of the Egyptian Mathematical Society","volume":"75 ","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some properties for meromorphic functions associated with integral operators\",\"authors\":\"W. Y. Kota, R. M. El-Ashwah\",\"doi\":\"10.1186/s42787-023-00163-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In the present paper we aim at proving some subordinations properties for meromorphic functions analytic in the punctured unit disc $$\\\\Delta ^*=\\\\{z:0<|z|<1\\\\}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow> <mml:msup> <mml:mi>Δ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>z</mml:mi> <mml:mo>:</mml:mo> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mo>|</mml:mo> <mml:mi>z</mml:mi> <mml:mo>|</mml:mo> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> with a simple pole at the origin. The functions under investigation are associated with two integral operators $$\\\\mathcal {P}_\\\\sigma ^\\\\gamma$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msubsup> <mml:mi>P</mml:mi> <mml:mi>σ</mml:mi> <mml:mi>γ</mml:mi> </mml:msubsup> </mml:math> and $$\\\\mathcal {Q}_\\\\sigma ^\\\\gamma$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msubsup> <mml:mi>Q</mml:mi> <mml:mi>σ</mml:mi> <mml:mi>γ</mml:mi> </mml:msubsup> </mml:math> (see Lashin in Comput Math Appl 59:524–531, 2010, https://doi.org/10.1016/j.camwa.2009.06.015 ). Several other results and numerical examples are also obtained.\",\"PeriodicalId\":33345,\"journal\":{\"name\":\"Journal of the Egyptian Mathematical Society\",\"volume\":\"75 \",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Egyptian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1186/s42787-023-00163-4\",\"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 the Egyptian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s42787-023-00163-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
摘要本文旨在证明穿孔单位盘上解析亚纯函数的一些从属性质$$\Delta ^*=\{z:0<|z|<1\}$$ Δ∗= {z: 0 ＆lt;| z | ＆lt;1}在原点有一个简单的极点。所研究的函数与两个积分算子$$\mathcal {P}_\sigma ^\gamma$$ P σ γ和$$\mathcal {Q}_\sigma ^\gamma$$ Q σ γ相关联(参见Lashin在计算数学应用59:524-531,2010,https://doi.org/10.1016/j.camwa.2009.06.015)。还得到了其他一些结果和数值算例。
Some properties for meromorphic functions associated with integral operators
Abstract In the present paper we aim at proving some subordinations properties for meromorphic functions analytic in the punctured unit disc $$\Delta ^*=\{z:0<|z|<1\}$$ Δ∗={z:0<|z|<1} with a simple pole at the origin. The functions under investigation are associated with two integral operators $$\mathcal {P}_\sigma ^\gamma$$ Pσγ and $$\mathcal {Q}_\sigma ^\gamma$$ Qσγ (see Lashin in Comput Math Appl 59:524–531, 2010, https://doi.org/10.1016/j.camwa.2009.06.015 ). Several other results and numerical examples are also obtained.
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