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 ∆ = {z ∈ c : |z| < 1} related with bernoulli’s lemniscate and obtained certain coefficient estimates, fekete-szegő inequality results for f ∈ mq(ϑ, φ). as a special case of our result, we obtain fekete-szegő inequality for a class of functions defined through poisson distribution and further with the help of maple— tm software we find hankel determinant inequality for f ∈ mq(ϑ, φ). our investigation generalises some previous results obtained in different articles.