Initial Bounds for Certain Classes of Bi-Univalent Functions Defined by Horadam Polynomials
Chinnaswamy Abirami, N. Magesh, Jagadeesan Yamini
Abstract
The main purpose of this article is to make use of the Horadam polynomials <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mfenced separators="" open="(" close=")"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> and the generating function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi mathvariant="normal">Π</mml:mi><mml:mfenced separators="" open="(" close=")"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>, in order to introduce three new subclasses of the bi-univalent function class <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>σ</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math> For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete–Szegö inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations.