{"title":"关于 $$ {\\mathbb {C}}^n $$ 中全态函数总衍生物的正态性标准","authors":"Molla Basir Ahamed, Sanju Mandal","doi":"10.1007/s40315-024-00523-w","DOIUrl":null,"url":null,"abstract":"<p>This paper continues investigation of conditions involving values shared by holomorphic functions and their total derivatives which imply the normality for a family of holomorphic functions concerning the total derivatives in <span>\\( {\\mathbb {C}}^n \\)</span>. Consequently, we obtain normality criterion of a family <span>\\( {\\mathcal {F}} \\)</span> of holomorphic functions <i>f</i>, where each function shares complex values with their linear total differential polynomials <span>\\( L_D^k(f) \\)</span> in <span>\\( {\\mathbb {C}}^n \\)</span>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"106 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Normality Criterion Concerning Total Derivatives of Holomorphic Functions in $$ {\\\\mathbb {C}}^n $$\",\"authors\":\"Molla Basir Ahamed, Sanju Mandal\",\"doi\":\"10.1007/s40315-024-00523-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper continues investigation of conditions involving values shared by holomorphic functions and their total derivatives which imply the normality for a family of holomorphic functions concerning the total derivatives in <span>\\\\( {\\\\mathbb {C}}^n \\\\)</span>. Consequently, we obtain normality criterion of a family <span>\\\\( {\\\\mathcal {F}} \\\\)</span> of holomorphic functions <i>f</i>, where each function shares complex values with their linear total differential polynomials <span>\\\\( L_D^k(f) \\\\)</span> in <span>\\\\( {\\\\mathbb {C}}^n \\\\)</span>.</p>\",\"PeriodicalId\":49088,\"journal\":{\"name\":\"Computational Methods and Function Theory\",\"volume\":\"106 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods and Function Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40315-024-00523-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods and Function Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00523-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Normality Criterion Concerning Total Derivatives of Holomorphic Functions in $$ {\mathbb {C}}^n $$
This paper continues investigation of conditions involving values shared by holomorphic functions and their total derivatives which imply the normality for a family of holomorphic functions concerning the total derivatives in \( {\mathbb {C}}^n \). Consequently, we obtain normality criterion of a family \( {\mathcal {F}} \) of holomorphic functions f, where each function shares complex values with their linear total differential polynomials \( L_D^k(f) \) in \( {\mathbb {C}}^n \).
期刊介绍:
CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.