a. k. wanas

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.

In this paper, we discuss the upper bounds for the second Hankel determinant 𝐻2(2) of a new subclass of 𝜆-pseudo-starlike bi-univalent functions defined in the open unit disk 𝑈.

The purpose of the present paper is to introduce and investigate two new subclasses 𝒦𝛴𝑚(𝜆,𝛾;𝛼) and 𝒦∗𝛴𝑚(𝜆,𝛾;𝛽) of 𝛴𝑚 consisting of analytic and 𝑚-fold symmetric bi-univalent functions defined in the open unit disk 𝑈. We obtain upper bounds for the coefficients |𝑎𝑚+1| and |𝑎𝑚| for functions belonging to these subclasses. Many of the well-known and new results are shown to follow as special cases of our results.