{"title":"A Characterization of Concave Mappings Using the Carathéodory Class and Schwarzian Derivative","authors":"Víctor Bravo, Rodrigo Hernández, Osvaldo Venegas","doi":"10.1007/s40315-024-00557-0","DOIUrl":null,"url":null,"abstract":"<p>The purpose of this paper is to establish new characterizations of concave functions <i>f</i> defined in <span>\\({\\mathbb {D}}\\)</span> in terms of the operator <span>\\(1+zf''/f'\\)</span>, the Schwarzian derivative and the lower order. We will distinguish the cases when the omitted set is bounded or unbounded, and in the latter case, we will address the subclasses determined by the angle at infinity.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"39 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-08-22","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/s40315-024-00557-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The purpose of this paper is to establish new characterizations of concave functions f defined in \({\mathbb {D}}\) in terms of the operator \(1+zf''/f'\), the Schwarzian derivative and the lower order. We will distinguish the cases when the omitted set is bounded or unbounded, and in the latter case, we will address the subclasses determined by the angle at infinity.
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.