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

Document Type : Research Paper

Authors

1 Dr. G. Murugusundaramoorthy, Ph.D. Sr.Professor of Mathematics, School of Advanced Sciences, VIT University, Vellore 632 014 India

2 Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria

3 Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria

Abstract

In this paper, we define new subclasses ${S}^{*}_{q}(\alpha,\Phi),$ ${M}_{q}(\alpha,\Phi)$ and ${L}_{q}(\alpha,\Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete-Szego inequalities. Further, we discuss the improved results for the associated classes involving subordination and majorization results briefly.

Keywords