On Convex Combinations of Starlike and Convex Functions Associated with the Epicycloid Domain Nur Athirah Hani Senin1,∗ , Yuzaimi Yunus2 , Nur Hazwani Aqilah Abdul Wahid3 , Rashidah Omar4 1Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Melaka, Kampus Bandaraya Melaka, 75350 Melaka, Malaysia 2Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Melaka, Kampus Jasin, 77300 Melaka, Malaysia 3Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia 4Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Sabah, 88450 Kota Kinabalu, Malaysia Emails: athirahhani1301@gmail.com; yuzaimi@uitm.edu.my; hazwaniaqilah@uitm.edu.my; rashidaho@uitm.edu.my Abstract This paper introduces the class Mε,4L, defined through a convex combination of starlike and convex functions associated with a four-cusped epicycloid domain, where the parameter satisfies 0 ≤ ε ≤ 1. Unlike earlier studies that focused on circular or conic domains, this work extends the geometric framework to epicycloidal domains. Within this framework, sharp estimates for the first coefficients are obtained, together with the Fekete-Szego inequality and the second Hankel determinant evaluations. These findings extend several classi- ¨ cal results for starlike and convex functions and offer new perspectives on analytic function theory related to epicycloidal domains. Keywords: ε-convex functions; epicycloid domain; univalent functions; coefficient bounds; Fekete–Szego¨ inequality; Hankel determinant