Abstract
References
- [1] Z. Abdulhadi, Typically real log-harmonic mappings, Int. J. Math. Math. Sci. 31, 1–9, 2002.
- [2] Z. Abdulhadi, Close-to-starlike log-harmonic mappings, Int. J. Math. Math. Sci. 19, 563–574, 1996.
- [3] Z. Abdulhadi and D. Bshouty, Univalent functions in $H\overline{H}(\mathbb{D})$, Tran. Amer. Math. Soc. 305, 841–849, 1988.
- [4] Z. Abdulhadi and Y. Abu Muhanna, Starlike log-harmonic mappings of order alpha, J. Inequal. Pure Appl. Math. 7, Article 123, 2006.
- [5] Z. Abdulhadi and W. Hengartner, Spirallike log-harmonic mappings, Complex Variables: Theory Appl. 9, 121–130, 1987.
- [6] Z. Abdulhadi and W. Hengartner, One pointed univalent log-harmonic mappings, J. Math. Anal. Appl. 203 , 333–351, 1996.
- [7] N. E. Cho, V. Kumar, S. S. Kumar and V. Ravichandran, Radius problems for starlike functions associated with the sine function, Bull. Iranian Math. Soc. 45, 213–232, 2019.
- [8] P. L. Duren, Univalent functions, Springer, New York, 1983.
- [9] W. Janowski, Some extremal problems for certain families of analytic functions I, Ann. Polon. Math. 28, 297–326, 1973.
- [10] Z. Liu and S. Ponnusamy, Some properties of univalent log-harmonic mappings, Filomat, 32, 5275–5288, 2018.
- [11] W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157–169, Conf. Proc. Lecture Notes Anal., I Int. Press, Cambridge, MA.
Abstract
In this paper, we define new subclasses $\mathcal{ST}_{lh}(s)$ and $\mathcal{CST}_{lh}(s)$ of sine starlike log-harmonic mappings and sine close-to-starlike log-harmonic mappings, respectively, defined in the open unit disc ${\mathbb D}$. We investigate representation theorem and integral representation theorem for functions in the class $\mathcal{ST}_{lh}(s)$. Further, we determine radius of starlikeness for functions in the classes $\mathcal{ST}_{lh}(s)$ and $\mathcal{CST}_{lh}(s)$.
Keywords
starlike function sine starlike log-harmonic mapping radius of starlikeness sine close-to-starlike log-harmonic mapping
References
- [1] Z. Abdulhadi, Typically real log-harmonic mappings, Int. J. Math. Math. Sci. 31, 1–9, 2002.
- [2] Z. Abdulhadi, Close-to-starlike log-harmonic mappings, Int. J. Math. Math. Sci. 19, 563–574, 1996.
- [3] Z. Abdulhadi and D. Bshouty, Univalent functions in $H\overline{H}(\mathbb{D})$, Tran. Amer. Math. Soc. 305, 841–849, 1988.
- [4] Z. Abdulhadi and Y. Abu Muhanna, Starlike log-harmonic mappings of order alpha, J. Inequal. Pure Appl. Math. 7, Article 123, 2006.
- [5] Z. Abdulhadi and W. Hengartner, Spirallike log-harmonic mappings, Complex Variables: Theory Appl. 9, 121–130, 1987.
- [6] Z. Abdulhadi and W. Hengartner, One pointed univalent log-harmonic mappings, J. Math. Anal. Appl. 203 , 333–351, 1996.
- [7] N. E. Cho, V. Kumar, S. S. Kumar and V. Ravichandran, Radius problems for starlike functions associated with the sine function, Bull. Iranian Math. Soc. 45, 213–232, 2019.
- [8] P. L. Duren, Univalent functions, Springer, New York, 1983.
- [9] W. Janowski, Some extremal problems for certain families of analytic functions I, Ann. Polon. Math. 28, 297–326, 1973.
- [10] Z. Liu and S. Ponnusamy, Some properties of univalent log-harmonic mappings, Filomat, 32, 5275–5288, 2018.
- [11] W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157–169, Conf. Proc. Lecture Notes Anal., I Int. Press, Cambridge, MA.
Details
| Primary Language | English |
|---|---|
| Subjects | Real and Complex Functions (Incl. Several Variables) |
| Journal Section | Mathematics |
| Authors | |
| Early Pub Date | April 14, 2024 |
| Publication Date | April 28, 2025 |
| Submission Date | November 4, 2023 |
| Acceptance Date | March 12, 2024 |
| Published in Issue | Year 2025 |