On q-ANALOGUE of Differential Subordination Associated with Lemniscate of Bernoulli

Abstract

This article comprises the study of differential subordination with analogue of q-derivative. It includes the sufficient condition on γ for 1+γ∂zqhz/hnz to be subordinated by 1+Az/1+Bz, −1≤B<A≤1, and implies that hz≺1+z, where hz is the analytic function in the open unit disk. Moreover, certain sufficient conditions for q-starlikeness of analytic functions related with lemniscate of Bernoulli are determined.