Applications of Modified Sigmoid Functions to a Class of Starlike Functions

Abstract

The main focus of this investigation is the applications of modified sigmoid functions. Due to its various uses in physics, engineering, and computer science, we discuss several geometric properties like necessary and sufficient conditions in the form of convolutions for functions to be in the special class <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msubsup><a:mrow><a:mi mathvariant="script">S</a:mi></a:mrow><a:mrow><a:mi>S</a:mi><a:mi>G</a:mi></a:mrow><a:mrow><a:mo>∗</a:mo></a:mrow></a:msubsup></a:math> earlier introduced by Goel and Kumar and obtaining third-order Hankel determinant for this class using modified sigmoid functions. Also, the third-order Hankel determinant for 2- and 3-fold symmetric functions of this class is evaluated.