Bohr phenomenon for certain close-to-convex analytic functions

[2008.00187] Bohr phenomenon for certain close-to-convex analytic functions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Complex Variables arXiv:2008.00187 (math) [Submitted on 1 Aug 2020 ( v1 ), last revised 14 Sep 2020 (this version, v2)] Title: Bohr phenomenon for certain close-to-convex analytic functions Authors: Vasudevarao Allu , Himadri Halder View a PDF of the paper titled Bohr phenomenon for certain close-to-convex analytic functions, by Vasudevarao Allu and Himadri Halder View PDF HTML (experimental) Abstract: We say that a class $\mathcal{B}$ of analytic functions $f$ of the form $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if for the largest radius $R_{f}<1$, the following inequality $$ \sum\limits_{n=1}^{\infty} |a_{n}z^{n}| \leq d(f(0),\partial f(\mathbb{D}) ) $$ holds for $|z|=r\leq R_{f}$ and for all functions $f \in \mathcal{B}$. The largest radius $R_{f}$ is called Bohr radius for the class $\mathcal{B}$. In this article, we obtain Bohr radius for certain subclasses of close-to-convex analytic functions. We establish the Bohr phenomenon for certain analytic classes $\mathcal{S}_{c}^{*}(\phi),\,\mathcal{C}_{c}(\phi),\, \mathcal{C}_{s}^{*}(\phi),\, \mathcal{K}_{s}(\phi)$. Using Bohr phenomenon for subordination classes \cite[Lemma 1]{bhowmik-2018}, we obtain some radius $R_{f}$ such that Bohr phenomenon for these classes holds for $|z|=r\leq R_{f}$. Generally, in this case $R_{f}$ need not be sharp, but we show that under some additional conditions on $\phi$, the radius $R_{f}$ becomes sharp bound. As a consequence of these results, we obtain several interesting corollaries on Bohr phenomenon for the aforesaid classes. Comments: 18 pages Subjects: Complex Variables (math.CV) MSC classes: 30C45, 30C50, 30C80 Cite as: arXiv:2008.00187 [math.CV] (or arXiv:2008.00187v2 [math.CV] for this version) https://doi.org/10.48550/arXiv.2008.00187 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Computational Methods and Function Theory 22 (2022), 491--517 Related DOI : https://doi.org/10.1007/s40315-021-00412-6 Focus to learn more DOI(s) linking to related resources Submission history From: Himadri Halder [ view email ] [v1] Sat, 1 Aug 2020 06:32:20 UTC (20 KB) [v2] Mon, 14 Sep 2020 15:14:46 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Bohr phenomenon for certain close-to-convex analytic functions, by Vasudevarao Allu and Himadri Halder View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2020-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from

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