Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions
DOI :
https://doi.org/10.5269/bspm.41077Résumé
‎In this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.
Références
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11. Srivastava, H. M., Mishra, A. K., Gochhayat, P, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23, 1188-1192, (2010).
12. Srivastava, H. M., Bulut, S, Caglar, M, Yagmur, N, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27, 831-842, (2013).
13. Srivastava, H. M., Sivasubramanian, S, Sivakumar, R, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, J. Tbilisi Math. 7, 1-10, (2014).
14. Srivastava, H. M., Gaboury, S, Ghanim, F, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. 36, 863-871, (2016).
15. Sumer Eker, S, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions. J. Turkish Math. 40, 641-646, (2016).
16. Xu, Q. H., Gui, Y. C., Srivastava, H. M., Coefficient estimates for a Certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25, 990-994, (2012).
17. Xu, Q. H., Xiao, H. G., Srivastava, H. M., A certain general subclass of analytic and biunivalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218, 11461-11465, (2012).
2. Bulut, S, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Math. Acad. Sci. Paris. 352, 479-484, (2014).
3. Caglar, M, Orhan, H, Yagmur, N, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27, 1165-1171, (2013).
4. Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, (1983).
5. Frasin, B. A., Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24, 1569-1573, (2011).
6. Kedzierawski, A. W., Some remarks on bi-univalent functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A. 39, 77-81, (1985).
7. Koepf, W., Coefficients of symmetric functions of bounded boundary rotations, Proc. Amer. Math. Soc. 105, 324-329, (1989).
8. Lewin, M, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18, 63-68, (1967).
9. Pommerenke, C, On the coefficients of close-to-convex functions, J. Michigan Math. 9, 259-269, (1962).
10. Ruscheweyh, S, New criteria for univalent functions, Proc. Amer. Math. Soc. 49, 109-115, (1975).
11. Srivastava, H. M., Mishra, A. K., Gochhayat, P, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23, 1188-1192, (2010).
12. Srivastava, H. M., Bulut, S, Caglar, M, Yagmur, N, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27, 831-842, (2013).
13. Srivastava, H. M., Sivasubramanian, S, Sivakumar, R, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, J. Tbilisi Math. 7, 1-10, (2014).
14. Srivastava, H. M., Gaboury, S, Ghanim, F, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. 36, 863-871, (2016).
15. Sumer Eker, S, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions. J. Turkish Math. 40, 641-646, (2016).
16. Xu, Q. H., Gui, Y. C., Srivastava, H. M., Coefficient estimates for a Certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25, 990-994, (2012).
17. Xu, Q. H., Xiao, H. G., Srivastava, H. M., A certain general subclass of analytic and biunivalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218, 11461-11465, (2012).
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2020-10-10
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