Fekete-Szeg"o problems for analytic functions in the space of logistic sigmoid functions based on quasi-subordination

In this paper, we define new subclasses S∗q(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--Szeg\"o inequalities. Further, we discuss the improved results for the associated classes involving subordination and majorization results briefly.