International Journal of Nonlinear Analysis and Applications

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

Document Type : Research Paper

Authors

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

Abstract

Using the q-calculus operator we defined a new subclass of analytic functions Mq(ϑ,Φ) defined in the open unit disk Δ={z∈C:|z|<1} related with Bernoulli's lemniscate and obtained certain coefficient estimates, Fekete-Szeg\H{o} inequality results for f∈Mq(ϑ,Φ). 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∈Mq(ϑ,Φ). Our investigation generalises some previous results obtained in different articles.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 237-251
  • Receive Date: 06 July 2020
  • Revise Date: 06 September 2020
  • Accept Date: 13 September 2020