Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor–Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients $\left|a_2\right|$ , $\left|a_3\right|$ and $\left|a_4\right|$ of the functions in the newly defined classes are given. Obtaining Fekete–Szegő inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete–Szegő functional is obtained for each of the three classes.

In this paper we introduce and investigate new classes of bi-Bazilevič functions of Ma-Minda type involving the Sălăgean integro-differential operator. Bounds of the first three coefficients |a2|, |a3...

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate certain special cases for our results.

In the current work, we use the (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve a linear combination between Bazilevic functions and ?-pseudo-starlike function defined in the unit disk D and establish upper bounds for the second and third coefficients of functions belongs to this new family. Also, we discuss Fekete-Szeg? problem in this new family.

In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the $\lambda$-pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices $T_2\left(2\right)$, $T_2\left(3\right)$, $T_3\left(1\right)$ and $T_3\left(2\right)$ for the functions in this family. Further, we investigate several special cases and consequences of our results.