Coefficient Inequalities and Geometric Behavior of a Sakaguchi-Type Bi-Univalent Class Associated with the Four-Leaf Domain
ax, cilt.15, sa.143, ss.1-16, 2026 (Hakemli Dergi)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15 Sayı: 143
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/axioms15060453
- Dergi Adı: ax
- Sayfa Sayıları: ss.1-16
- Kocaeli Üniversitesi Adresli: Evet
Özet
Abstract
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 , whose image is a four-leaf-shaped domain. For suitable choices of the complex parameter b with , , and the real parameters and , we study the class of bi-univalent functions f for which both f and its inverse satisfy a Sakaguchi-type subordination condition involving the fundamental ratios and together with the difference quotient .
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
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.