In this paper, we define new subclasses Sq ∗ (α, Φ), Mq (α, Φ) and Lq (α, Φ) of analytic functions in the space of logistic sigmoid functions based on quasi–subordination and determine the initial coefficient estimates |a2| and |a3| and also determine the relevant connection to the classical Fekete–Szegö inequalities. Further, we discuss the improved results for the associated classes involving subordination and majorization results briefly. © 2018, Semnan University, Center of Excellence in Nonlinear Analysis and Applications. All rights reserved.