{"title":"对数-对数解析函数的进展:朗道类型定理及其完善","authors":"Hanghang Zhao, Ming-Sheng Liu, Kit Ian Kou","doi":"arxiv-2409.09624","DOIUrl":null,"url":null,"abstract":"This work begins by introducing the groundbreaking concept of log-p-analytic\nfunctions. Following this introduction, we proceed to delineate four distinct\nformulations of Landau-type theorems, specifically crafted for the domain of\npoly-analytic functions. Among these, two theorems are distinguished by their\nexactitude, and a third theorem offers a refinement to the existing work of\nAbdulhadi and Hajj. Concluding the paper, we present four specialized versions\nof Landau-type theorems applicable to a subset of bounded log-p-analytic\nfunctions, resulting in the derivation of two precise outcomes.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Advancements in Log-P-Analytic Functions: Landau-Type Theorems and Their Refinements\",\"authors\":\"Hanghang Zhao, Ming-Sheng Liu, Kit Ian Kou\",\"doi\":\"arxiv-2409.09624\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work begins by introducing the groundbreaking concept of log-p-analytic\\nfunctions. Following this introduction, we proceed to delineate four distinct\\nformulations of Landau-type theorems, specifically crafted for the domain of\\npoly-analytic functions. Among these, two theorems are distinguished by their\\nexactitude, and a third theorem offers a refinement to the existing work of\\nAbdulhadi and Hajj. Concluding the paper, we present four specialized versions\\nof Landau-type theorems applicable to a subset of bounded log-p-analytic\\nfunctions, resulting in the derivation of two precise outcomes.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09624\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09624","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Advancements in Log-P-Analytic Functions: Landau-Type Theorems and Their Refinements
This work begins by introducing the groundbreaking concept of log-p-analytic
functions. Following this introduction, we proceed to delineate four distinct
formulations of Landau-type theorems, specifically crafted for the domain of
poly-analytic functions. Among these, two theorems are distinguished by their
exactitude, and a third theorem offers a refinement to the existing work of
Abdulhadi and Hajj. Concluding the paper, we present four specialized versions
of Landau-type theorems applicable to a subset of bounded log-p-analytic
functions, resulting in the derivation of two precise outcomes.