{"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}
引用次数: 0
Abstract
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.