On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator
Abstract
:1. Introduction
2. A Set of Lemmas
3. Upper Bound for the Second Hankel Determinant
4. Some Results on Third Hankel Determinants and Their Upper Bounds
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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El-Ityan, M.; Shakir, Q.A.; Al-Hawary, T.; Buti, R.; Breaz, D.; Cotîrlă, L.-I. On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator. Mathematics 2025, 13, 1269. https://doi.org/10.3390/math13081269
El-Ityan M, Shakir QA, Al-Hawary T, Buti R, Breaz D, Cotîrlă L-I. On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator. Mathematics. 2025; 13(8):1269. https://doi.org/10.3390/math13081269
Chicago/Turabian StyleEl-Ityan, Mohammad, Qasim Ali Shakir, Tariq Al-Hawary, Rafid Buti, Daniel Breaz, and Luminita-Ioana Cotîrlă. 2025. "On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator" Mathematics 13, no. 8: 1269. https://doi.org/10.3390/math13081269
APA StyleEl-Ityan, M., Shakir, Q. A., Al-Hawary, T., Buti, R., Breaz, D., & Cotîrlă, L.-I. (2025). On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (p,q)-Derivative Operator. Mathematics, 13(8), 1269. https://doi.org/10.3390/math13081269