Coefficient Inequalities and Geometric Behavior of a Sakaguchi-Type Bi-Univalent Class Associated with the Four-Leaf Domain

The main objective of this paper is to introduce and investigate a new subclass of Sakaguchi-type analytic bi-univalent functions in the open unit disk, defined by a two-sided subordination condition to the four-leaf function Λ4L(z)=1+56z+16z5, whose image is a four-leaf-shaped domain. For suitable choices of the complex parameter b with |b|≤1, b≠1, and the real parameters α∈[0,1] and ρ≥0, we study the class GΣ,bα,ρ(Λ4L) of bi-univalent functions f for which both f and its inverse g=f−1 satisfy a Sakaguchi-type subordination condition involving the fundamental ratios f(z)/z and f′(z) together with the difference quotient f(z)−f(bz)−1. Coefficient inequalities for the initial Taylor–Maclaurin coefficients are obtained, and Fekete–Szegő-type estimates are derived for the associated coefficient functional. Furthermore, graphical representations of the image domains are provided, which illustrate the geometric behavior of the functions in GΣ,bα,ρ(Λ4L) and confirm that the proposed class is non-trivial. The present investigation extends recent studies on subclasses of analytic and bi-univalent functions associated with geometrically structured mappings and contributes to the visual interpretation of their analytic properties.