Sharpened bounds for the Caratheodory function associated with the generating function of the Lucas-balancing polynomials

Mohmmed, Zainab Aodeh A.; Gebur, Semh Kadhim

doi:10.47974/JIM-2558

Open Access Research Article

Sharpened bounds for the Caratheodory function associated with the generating function of the Lucas-balancing polynomials

^*Zainab Aodeh A. MohmmedCorresponding authorzainab.aodeh@qu.edu.iqDepartment of Mathematics College of Education University of Al-QadisiyahDiwaniya, IraqView full profile → , Semh Kadhim Gebursemh.Alisawi@qu.edu.iqDepartment of Mathematics College of Education University of Al-QadisiyahDiwaniya, IraqView full profile →

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pp. 1655–1662Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2558XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2558
Pages:: 1655–1662

Abstract

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|<1}, where 𝒯 has the property 𝒯(𝔄) = 𝔄. We gave results about inequalities involving the module for |𝒯’ (a)| in case the zero of the function (𝒯(z) – 1) are different from zero in the disk A, We relied on those results on the first non-zero the taylor’s coefficients 𝒹1 and 𝒹1.

Keywords

Boundary schwarz lemma Unit disk Zeros Analytic functions Angular limits Derivative estimates Maximum principle Carathéodory functions Lucas–balancing polynomials

Subject Classifications

30C4533C45

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