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

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.