Coefficient Inequalities and Geometric Behavior of a Sakaguchi-Type Bi-Univalent Class Associated with the Four-Leaf Domain
AXIOMS, cilt.15, sa.6, 2026 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15 Sayı: 6
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/axioms15060453
- Dergi Adı: AXIOMS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
- Kocaeli Üniversitesi Adresli: Evet
Özet
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 Lambda 4L(z)=1+56z+16z5, whose image is a four-leaf-shaped domain. For suitable choices of the complex parameter b with |b|<= 1, b not equal 1, and the real parameters alpha is an element of[0,1] and rho >= 0, we study the class G Sigma,b alpha,rho(Lambda 4L) 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-Szeg & odblac;-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 G Sigma,b alpha,rho(Lambda 4L) 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.