Communications of the
Korean Mathematical Society CKMS

In this paper, a new subclass, $\mathcal{SC}_{\sigma}^{\mu,{p},{q}}({r},{s};x)$, of Sakaguchi-type analytic bi-univalent functions defined by $({p},{q})$-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for $|a_{2}|$ and $|a_{3}|$ are obtained. Fekete-Szeg\"{o} inequalities for the class are found. Finally, we give some corollaries.

Keywords: Analytic functions, univalent functions, bi-univalent functions, Fekete-Szeg\"{o} problem, Sakaguchi-type functions, $({p},{q})$-derivative operator, Horadam polynomials

MSC numbers: Primary 30C45, 30C15