Certain Class of Starlike Functions Associated with Modified Sigmoid Function

Let S-SG* = {f. A : z f' is an element of (z)/f (z) < 2/(1 + e(-z))}. For this class, several radius estimates and coefficient bounds are obtained as well as structural formula, growth theorem, distortion theorem and inclusion relations are established. Further, let p be an analytic function such that p(0) = 1. Sharp bounds on beta is an element of R are determined for various first-order differential subordinations such as 1 + beta zp' (z)/p(k) (z), p(z) + beta zp' ( z)/p(k) (z) < 2/(1 + e(-z)) to imply that p(z) < (1 + Az)/(1 + Bz), where -1 <= B < A <= 1 or root 1 + z and also when the position of dominants is interchanged. Moreover, these results are extended by considering beta to be a complex number.