journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-2558 Sharpened bounds for the Caratheodory function associated with the generating function of the Lucas-balancing polynomials Mohmmed Zainab Aodeh A. Department of Mathematics, College of Education, University of Al-Qadisiyah, Diwaniya, Iraq Gebur Semh Kadhim Department of Mathematics, College of Education, University of Al-Qadisiyah, Diwaniya, Iraq 29 5-B 1655 1662 27 06 2026

The lower bounds of |𝒯’ (a)| were estimated for an analytic function 𝒯 with an angular limit at a boundary point on the unit disk 𝔄 = {z ∈ C:|z|

 Boundary schwarz lemma Unit disk Zeros Analytic functions Angular limits Derivative estimates Maximum principle Carathéodory functions Lucas–balancing polynomials access open retracted no