Initial Coefficient Estimates for New Families of m-Fold Symmetric Bi-univalent Functions
Abstract
In the present work, we define two new families of analytic and m-fold symmetric biunivalent functions in the open unit disk $\Delta$. Also, for functions in each of the classes introduced here, we prove upper bounds for the initial coefficients $\left|b_{m+1}\right|$ and $\left|b_{2 m+1}\right|$. Furthermore, we get new special cases for our results.
References
Ş. Altinkaya and S. Yalçin, Coefficient bounds for certain subclasses of m-fold symmetric biunivalent functions, J. of Math., vol. 2015, Article ID 241683, 5 pp. https://doi.org/10.1155/2015/241683
W. G. Atshan and N. A. J. Al-Ziadi, Coefficients bounds for a general subclasses of m-fold symmetric bi-univalent functions, J. Al-Qadisiyah Comput. Sci. Math. 9(2) (2017), 33-39. https://doi.org/10.29304/jqcm.2017.9.2.141
D. Brannan and J. G. Clunie (Eds), Aspects of contemporary complex analysis, (Proceedings of the NATO advanced study institute held at the Univ. of Durham, Durham; July 1-20, 1979), New York, London : Academic Press, 1980.
P. L. Duren, Univalent Functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1983.
W. Koepf, Coefficients of symmetric functions of bounded boundary rotations, Proc. Amer. Math. Soc. 105 (1989), 324-329. https://doi.org/10.1090/S0002-9939-1989-0930244-7
T. R. K. Kumar, S. Karthikeyan, S. Vijayakumar and G. Ganapathy, Initial coefficient estimates for certain subclasses of m-fold symmetric bi-univalent functions, Advances in Dynamical Systems and Applications 16(2) (2021), 789-800. https://doi.org/10.34198/ejms.6221.209223
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68. https://doi.org/10.1090/s0002-9939-1967-0206255-1
X. Li and A. Wang, Two new subclasses of bi-univalent functions, International Math. Forum 7(30) (2012), 1495-1504.
G. Murugusundaramoorthy, N. Magesh and V. Prameela, Coefficient bounds for certain subclasses of bi-univalent functions, Abstract and Applied Analysis, vol. 2013, Article ID 573017, 3 pp. https://doi.org/10.1155/2013/573017
C. Pommerenke, On the coefficients of close-to-convex functions, Michigan Math. J. 9 (1962), 259-269.
A. M. Ramadhan and N. A. J. Al-Ziadi, Coefficient bounds for new subclasses of m-fold symmetric holomorphic bi-univalent functions, Earthline Journal of Mathematical Sciences 10(2) (2022), 227-239. https://doi.org/10.34198/ejms.10222.227239
S. Sivasubramanian and R. Sivakumar, Initial coefficient bound for m-fold symmetric bi-X-convex functions, J. Math. Inequalities 10(3) (2016), 783-791. https://doi.org/10.7153/jmi-10-63
H. M. Srivastava, S. Gaboury and F. Ghanim, Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Universitatis Apulensis 41 (2015), 153-164. https://doi.org/10.17114/j.aua.2015.41.12
H. M. Srivastava, S. Gaboury and F. Ghanim, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Mathematica Scientia 36(3) (2016), 863-871. https://doi.org/10.1016/S0252-9602(16)30045-5
H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23 (2010), 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009
H. M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Mathematical J. 7(2) (2014), 1-10. https://doi.org/10.2478/tmj-2014-0011
A. K. Wanas and H. Tang, Initial coefficient estimates for a classes of m-fold symmetric biunivalent functions involving Mittag-Leffler function, Mathematica Moravica 24(2) (2020), 51-61. https://doi.org/10.5937/matmor2002051k
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