Fekete-Szegӧ Inequality For Certain Subclass Of Multivalent Functions Associated with Al-Oboudi Differential Operator

In this paper, we define and study a new class of multivalent analytic functions defined on the open unit disk , where this class is defined by means of the Al-Aboudi differential operator. Given the importance of coefficient bounds in shaping the behavior of multivalent functions, the Fekete–Szegő inequality is used to derive the coefficient bounds for functions belonging to this class, in order to illustrate the role of the Al-Aboudi differential operator in influencing this behavior. This study also presents a unified framework that combines the Al-Aboudi differential operator with some classical results on coefficient bounds, leading to generalizations that serve as a foundation for subsequent developments in the theory of geometric functions