A Study of Certain Geometric Properties and Hardy Spaces of the Normalized Miller-Ross Function
Abstract
:1. Introduction
- A function if and only if
- A function if and only if
2. Relevant Lemmas
- (i).
- If , then
- (ii).
- If , then there exist such that
3. Starlikeness and Convexity of the Normalized Form of the Miller-Ross Function
- (i).
- ,
- (ii).
- hold, then the function belongs to the class in
4. Hardy Space of the Normalized Form of the Miller-Ross Function
- (i).
- If , then
- (ii).
- If , then
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Abubakr, M.; Raza, M.; Alenazi, A.; Mehrez, K. A Study of Certain Geometric Properties and Hardy Spaces of the Normalized Miller-Ross Function. Mathematics 2025, 13, 1919. https://doi.org/10.3390/math13121919
Abubakr M, Raza M, Alenazi A, Mehrez K. A Study of Certain Geometric Properties and Hardy Spaces of the Normalized Miller-Ross Function. Mathematics. 2025; 13(12):1919. https://doi.org/10.3390/math13121919
Chicago/Turabian StyleAbubakr, Muhammad, Mohsan Raza, Abdulaziz Alenazi, and Khaled Mehrez. 2025. "A Study of Certain Geometric Properties and Hardy Spaces of the Normalized Miller-Ross Function" Mathematics 13, no. 12: 1919. https://doi.org/10.3390/math13121919
APA StyleAbubakr, M., Raza, M., Alenazi, A., & Mehrez, K. (2025). A Study of Certain Geometric Properties and Hardy Spaces of the Normalized Miller-Ross Function. Mathematics, 13(12), 1919. https://doi.org/10.3390/math13121919