Some well-known authors have extensively used orthogonal polynomials in the framework of geometric function theory. We are motivated by previous research that has been conducted and, this study, we solve Fekete–Szegö problem as well give bound estimates for coefficients and an upper estimate second Hankel determinant functions class G?(v,?) analytical bi-univalent functions, implicating Euler p...

By using the q-derivative operator and Legendre polynomials, some new subclasses of q-starlike functions bi-univalent are introduced. Several coefficient estimates Fekete–Szegö-type inequalities for in each these obtained. The results derived this article shown to extend generalize those earlier works.

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc this work. provide estimates for first two Taylor–Maclaurin series coefficients these functions. Furthermore, we define Salagean differential operator and discuss various applications our main findings using it. A few well-known corollaries are studied order to show connection between recent earlier