Some Evaluations About Coefficients Boundaries for Specific Classes of Bi-Univalent Functions - Suliman M. Sowileh; Gangadharan Murugusundaramoorthy; Borhen Halouani; Ibrahim S. Elshazly; Mohamed A. Mamon; Alaa H. El-Qadeem (Axioms)
New subclasses of bi-univalent functions with bounded boundary rotation are presented in this study. We acquired estimates for the initial coefficients <semantics><mfenced separators="" open="|" close="|">a2</mfenced></semantics>, <semantics><mfenced separators="" open="|" close="|">a3</mfenced></semantics> and <semantics><mfenced separators="" open="|" close="|">a4</mfenced></semantics>. Furthermore, we have verified the specific situations satisfying the famous hypothesis of Brannan and Clunie. Additionally, we have obtained the well-known Fekete–Szegö inequality for the newly identified bi-univalent function subclasses. Our results not only improve, but also extend several existing results as particular cases.