On the Study of Bi-Univalent Functions Defined by the Generalized S\u{a}l\u{a}gean Differential Operator

Abstract

In this paper, we make use of the generalized S\u{a}l\u{a}gean differential operator to define a novel class of bi-univalent functions that is associated with the generalized hyperbolic sine function in the open unit disk  $\mathbb{D}$. The prime goal of this paper to derive sharp coefficient bounds in open unit disk $\mathbb{D}$, especially the first two coefficient bounds for the functions belong to this class . The investigation also focuses on studying the classical Fekete-Szeg\"{o} functional problem for functions belong to this class. Furthermore, some known corollaries are highlighted based on the unique choices of the parameters involved in this class.