Bi-Univalent Functions Associated with C-Shaped Domains

Abstract

Motivated by the geometric theory of analytic functions, this paper introduces two parameterized subclasses of bi-univalent functions through a subordination condition associated with a C-shaped domain. Sharp estimates for the initial Taylor coefficients are established, and corresponding Fekete–Szeg"o type inequalities are obtained. Furthermore, several special cases are discussed by assigning suitable values to the defining parameters, yielding a variety of new consequences for different families of bi-univalent functions. The obtained results not only unify and extend a number of existing coefficient estimates but also provide a flexible approach for investigating coefficient-related problems within the framework of geometric function theory.