Using a General Hurwitz-Lerch Zeta for BI-Univalent Analytic Functions to Estimate a Second Hankel Determinant
Using a General Hurwitz-Lerch Zeta for BI-Univalent Analytic Functions to Estimate a Second Hankel Determinant
Alaa Ali Aljamie1, Nagat Muftah Alabbar2*
1Mathematics Department, Faculty of Science, University of Derna, Derna, Libya.
2Mathematics Department, Faculty of Education of Benghazi, University of Benghazi.Libya.
Publication Information
Journal Title: International Journal of Research and Scientific Innovation (IJRSI)
Author(s):Aljamie, Alaa Ali ;Alabbar, Nagat Muftah
Published On: 08/06/2025
Volume: 12
Issue: 5
First Page: 1502
Last Page: 1511
ISSN: 2321-2705
Cite this Article Aljamie, Alaa Ali ;Alabbar, Nagat Muftah
; Using a General Hurwitz-Lerch Zeta for BI-Univalent Analytic Functions to Estimate a Second Hankel Determinant, Volume 12 Issue 5, International Journal of Research and Scientific Innovation (IJRSI), 1502-1511, Published on 08/06/2025, Available at https://rsisinternational.org/journals/ijrsi/articles/using-a-general-hurwitz-lerch-zeta-for-bi-univalent-analytic-functions-to-estimate-a-second-hankel-determinant/
Abstract
In this paper, we introduce and investigate a new class of bi- univalent functions defined in the open unit disk 
involving a general integral operator associated with the general Hurwitz- Lerch Zeta function denoted by 
. The main result of the investigation is to estimate the upper bounds for the initial Taylor–Maclaurin coefficients of functions 
and 
for this class. Following, we find the second Hankel determinant. Several new results are shown after specializing the parameters employed in our main results.
Keywords: Hankel determinant, Bi-univalent functions, coefficient bounds, Hurwitz -Lerch zeta function.
