A New Class of Generalized Starlike Bi-Univalent Functions Subordinated to Legendre Polynomials

A new class of generalized starlike bi-univalent functions is introduced in this paper, which is defined using Legendre Polynomials within the open unit disk D. This paper sheds a light on the properties and behaviors of these starlike bi-univalent functions, providing estimations for the modulus of the initial Taylor series coefficients of the functions falling under this particular class and one of its various subclasses. Additionally, this paper also investigates the classical Fekete-Szegö functional problem for functions f that are part of the aforementioned class. Moreover, we obtain the classical Fekete-Szegö inequalities of functions belonging to this class and to one of its various subclasses.