Document Type : Research Paper

Authors

• Murugusundaramoorthy Gangadharan ¹
• Sunday Oluwafemi Olatunji ²
• O.A. Fadipe-Joseph ³

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 $S_q^{\ast }(\alpha ,\mathrm{\Phi }),$ $M_q(\alpha ,\mathrm{\Phi })$ and $L_q(\alpha ,\mathrm{\Phi })$ 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

• univalent function
• starlike function
• quasi--subordination
• logistic sigmoid function
• Fekete-Szego inequality