Radius of concavity for certain class of functions

[2407.00457] Radius of concavity for certain class of functions Skip to main content Search Submit Donate Log in Mathematics > Complex Variables arXiv:2407.00457 (math) [Submitted on 29 Jun 2024 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Radius of concavity for certain class of functions Authors: Molla Basir Ahamed , Rajesh Hossain View PDF HTML (experimental) Abstract: Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In this paper, we find radius of concavity and compute the same for functions in $ \mathcal{S}(p) $ and for some other well-known classes of functions on unit disk. We explore general linear combinations $F(z):=\lambda_1f_1(z)+\cdots+\lambda_{2n} f_{2n}(z),\; \lambda_j\in\mathbb{C} $, $ n\in\mathbb{N} $, of functions belonging to the class $\mathcal{S}(p)$ and some other classes of functions of analytic univalent functions and investigate their radii of univalence, convexity and concavity. Subjects: Complex Variables (math.CV) MSC classes: 30C45, 30C55 Cite as: arXiv:2407.00457 [math.CV] (or arXiv:2407.00457v2 [math.CV] for this version) https://doi.org/10.48550/arXiv.2407.00457 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Molla Basir Ahamed [ view email ] [v1] Sat, 29 Jun 2024 15:11:25 UTC (14 KB) [v2] Fri, 28 Aug 2026 05:48:48 UTC (42 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2024-07 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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