Volume 27 , Issue 1 , PP: 234-245, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Nur Athirah Hani Senin 1 * , Yuzaimi Yunus 2 , Nur Hazwani Aqilah Abdul Wahid 3 * , Rashidah Omar 4
Doi: https://doi.org/10.54216/IJNS.270121
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-Szeg¨o inequality and the second Hankel determinant evaluations. These findings extend several classical results for starlike and convex functions and offer new perspectives on analytic function theory related to epicycloidal domains.
&epsilon , -convex functions , epicycloid domain , univalent functions , coefficient bounds , Fekete&ndash , Szeg¨ , o inequality , Hankel determinant
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