Sufficiency Criteria for Q-Starlike Functions Associated with Cardioid

This article deals with the q-differential subordinations for starlike functions associated with the lemniscate of Bernoulli and cardioid domain. The primary goal of this work is to find the conditions on γ for 1+γz∂q hz/hn z ≺1+z, where hz is analytic function and is subordinated by the function which is producing cardioid domain as its image domain while mapping the open unit disk. Along with this, certain sufficient conditions for q-starlikeness of analytic functions are determined.