Coefficient problems of bi-univalent functions with respect to symmetric and symmetric conjugate points defined by the Al-Oboudi operator

Abstract

We present and investigate two additional subclasses of bi-univalent functions corresponding to symmetric and symmetric conjugate points in the open unit disc employing the Al-Oboudi operator. The initial coefficients of functions assigned to these classes are estimated.

Bi-Univalent Function Classes Defined by Using an Einstein Function and a New Generalised Operator

“…In addition to estimating the coefficients for |a 2 | and |a 3 |, Brannan and Taha (1988) proposed the concepts of strongly bi-starlike functions of the order 𝛼 and strongly biconvex functions of the order 𝛼. Following the lead of Brannan and Taha (1988) , other researchers (Rossdy et al, 2021;Soni et al, 2018;Xu et al, 2012) have studied numerous subclasses of and determined the coefficient bounds for |a 2 | and |a 3 |.…”

“…Yet, there has been relatively little research and discovery on the relevant features involving bi-univalent function subclasses. However, much attention has been focused on bi-univalent functions' initial coefficients (Al-Ameedee et al, 2020;Rossdy et al, 2021;Soni et al, 2018). Gradshteyn and Ryzhik (2014) published a formulation for the Bernoulli polynomials in 1980, which has substantial uses in number theory and classical analysis.…”