Boundedness in the Bloch Space of Symmetric Domain for a Class of Multi-Valent Meromorphic Functions Given by a Fractional Integral
Abstract
:1. Background
2. Preliminaries
2.1. Definitions
- Two analytic functions are convoluted ( ) if
2.2. Fractional Operators
2.3. Convolution Operator
2.4. Lemmas
3. Analytic Results
3.1. Inclusion Outcomes
3.2. General Properties
3.3. Sandwich Outcomes
4. Boundedness Results
4.1. Boundedness in Bloch Space
4.2. Boundedness in Symmetrical Siegel Domain
4.3. Polar Derivative of the Partial Sums
- , where
- , where
- , where ;
- where .
- , where
- , where
- , where ;
- where .
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Aldawish, I.; Ibrahim, R.W. Boundedness in the Bloch Space of Symmetric Domain for a Class of Multi-Valent Meromorphic Functions Given by a Fractional Integral. Symmetry 2023, 15, 1761. https://doi.org/10.3390/sym15091761
Aldawish I, Ibrahim RW. Boundedness in the Bloch Space of Symmetric Domain for a Class of Multi-Valent Meromorphic Functions Given by a Fractional Integral. Symmetry. 2023; 15(9):1761. https://doi.org/10.3390/sym15091761
Chicago/Turabian StyleAldawish, Ibtisam, and Rabha W. Ibrahim. 2023. "Boundedness in the Bloch Space of Symmetric Domain for a Class of Multi-Valent Meromorphic Functions Given by a Fractional Integral" Symmetry 15, no. 9: 1761. https://doi.org/10.3390/sym15091761
APA StyleAldawish, I., & Ibrahim, R. W. (2023). Boundedness in the Bloch Space of Symmetric Domain for a Class of Multi-Valent Meromorphic Functions Given by a Fractional Integral. Symmetry, 15(9), 1761. https://doi.org/10.3390/sym15091761