Coefficient estimates for subclasses of analytic functions related to Bernoulli's lemniscate and an application of Poisson distribution series

Document Type : Research Paper


1 Department of Mathematics, SAS, Vellore Institute of Technology, deemed to be University, Vellore-632014, India

2 Faculty of Mathematics and Computer Science, Babes-Bolyai University, 400084 Cluj-Napoca, Romania


Using the $q$-calculus operator we defined a new subclass of analytic functions $\mathcal{M}_q(\vartheta,\Phi)$ defined in the open unit disk $\Delta=\{z\in\mathbb{C}:\left\vert z\right\vert<1\}$ related with Bernoulli's lemniscate and obtained certain coefficient estimates, Fekete-Szeg\H{o} inequality results for $f\in\mathcal{M}_q(\vartheta,\Phi)$. As a special case of our result, we obtain Fekete-Szeg\H{o} inequality for a class of functions defined through Poisson distribution and further with the help of MAPLE\texttrademark\ software we find Hankel determinant inequality for $f\in\mathcal{M}_q(\vartheta,\Phi)$. Our investigation generalises some previous results obtained in different articles.


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Volume 13, Issue 2
July 2022
Pages 237-251
  • Receive Date: 06 July 2020
  • Revise Date: 06 September 2020
  • Accept Date: 13 September 2020