The aim of this paper is to establish the coefficient estimates for the subclasses ofq-starlike andq-convex functions with respect to symmetric points involvingq-difference operator. Also certain applications based on these results for subclasses of univalent functions defined by convolution are given.

In this present investigation, we consider the subclass of analytic and bi-univalent functions associated with salagean operator consisting of the function class Σ in the unit open disk, which satisfies the qusi-subordination conditions. Also we obtain the first two Taylor-Maclaurin coefficients for functions in this new subclass.

By motivating the result of Ramachandran et al. [Certain results on q-starlike and q-convex error functions, Math. Slovaca, 68(2) (2018), 361–368], in this present investigation we derive the classical Fekete Szegö theorem for a close-to-convex error function of order β and the sharp estimates also obtained for real μ.

In this present article, we studied and examined the novel general subclasses of the function class $\Sigma$ of bi-univalent function defined in the open unit disk, which are associated with the Horadam polynomial. This study locates estimates on the Taylor - Maclaurin coefficients $|a_{2}|$ {\it and} $|a_{3}|$ in functions of the class which are considered. Additionally, Fekete-Szeg\"{o} inequality of functions belonging to this subclasses are also obtained.

In this present paper, our goal is to introduce two new subclasses of analytic bi-univalent functions defined by means of Horadam polynomials in the open unit disc U. Also we find initial estimates on Taylor-Maclaurin coefficients and provided the relevant Fekete-Szegö theorem using coefficient estimates for the defined new subclasses.