Fourth Hankel Determinant Problem Based on Certain Analytic Functions
Abstract
:1. Introduction
- For :
- For :Krishna [4] derived a precise estimate of for the class of Bazilevič functions. On the other hand the sharp bound of for the class of close-to-convex functions remains unknown.
- For :He also thought that the bounds were still not sharp. Later, in 2018, Kwon improved the Zaprawa inequality for by achieving , and in 2021, Zaprawa refined this bound even further by establishing that for . In the papers [7,8], the non-sharp bounds of this determinant for the sets and , respectively, were also computed. They succeeded in achieving:
- For :
2. A Set of Lemmas
3. Main Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Tang, H.; Arif, M.; Haq, M.; Khan, N.; Khan, M.; Ahmad, K.; Khan, B. Fourth Hankel Determinant Problem Based on Certain Analytic Functions. Symmetry 2022, 14, 663. https://doi.org/10.3390/sym14040663
Tang H, Arif M, Haq M, Khan N, Khan M, Ahmad K, Khan B. Fourth Hankel Determinant Problem Based on Certain Analytic Functions. Symmetry. 2022; 14(4):663. https://doi.org/10.3390/sym14040663
Chicago/Turabian StyleTang, Huo, Muhammad Arif, Mirajul Haq, Nazar Khan, Mustaqeem Khan, Khurshid Ahmad, and Bilal Khan. 2022. "Fourth Hankel Determinant Problem Based on Certain Analytic Functions" Symmetry 14, no. 4: 663. https://doi.org/10.3390/sym14040663