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

This article comprises the study of differential subordination with analogue of q -derivative. It includes the sufficient condition on γ for 1 + γ ∂ z q h z / h n z to be subordinated by 1 + A z / 1 + B z , − 1 ≤ B < A ≤ 1 , and implies that h z ≺ 1 + z , where h z 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.