Bounds for initial MacLaurin coefficients of a subclass of bi-univalent functions associated with subordination

Year 2019, Volume: 68 Issue: 1, 125 - 135, 01.02.2019

Ahmad Motamednezhad , Shahpour Nosrati Sima Zaker

https://doi.org/10.31801/cfsuasmas.443665

Cited By: 3

https://izlik.org/JA55SH98TE

Abstract

In this paper, we investigate the bounds of the coefficients for new subclasses of analytic and bi-univalent functions in the open unit disc defined by subordination. The coefficients bounds presented in this paper would generalize and improve those in related works of several earlier authors

Keywords

Analytic functions , bi-univalent functions , boefficient estimates , Hadamard product , subordination

References

• Brannan, D. A., Clunie J. and Kirwan, W. E., Coefficient estimates for a class of starlike functions, Can. J. Math. 22 (1970) 476-485.
• Brannan, D. A. and Taha, T.S., On some classes of bi-univalent functions, KFAS Proceedings Series, vol. 3, Pergamon Press (Elsevier Science Limited), Oxford, 1988, 53-60.
• Catas, A., Oros, G. I., Oros, G., Differential subordinations associated with multiplier transformations, Abstr. Appl. Anal. (2008), ID 845724:1-11.
• Chen, M., On the regular functions satisfying ℜ(f(z)/z)>α, Bull. Inst. Math. Acad. Sinica 3 (1975) 65-70.
• Chichra, P. N., New subclasses of the class of close-to-convex functions, Proc. Am. Math. Soc. (62) (1977) 37-43.
• Çaglar, M., Deniz, E. and Srivastava, H. M., Second Hankel determinant for certain subclasses of bi-univalent functions, Turkish J. Math. 41, (2017) 694-706.
• Ding, S. S., Ling Y. and Bao, G. J., Some properties of a class of analytic functions, J. Math. Anal. Appl. 195 (1) (1995) 71-81.
• Duren, P. L., [newblock]\newblock{\em Univalent Functions}, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
• Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999) 1-13.
• El-Ashwah, R. M., Subclasses of bi-univalent functions defined by convolution, J. Egypt. Math. Soc. (2013)
• Frasin B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011) 1569-1573.
• MacGregor, T. H., Functions whose derivative has a positive real part, Trans. Am. Math. Soc. 104 (1962) 532-537. Ch. : Pommerenke, C., Univalent Functions, Vandenhoeck and Rupercht, Gottingen, 1975.
• Porwal S. and Darus, M., On a new subclass of bi-univalent functions, J. Egyptian Math. Soc. 21, (2013) 190-193.
• Srivastava, H. M., Mishra A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188-1192.
• Srivastava, H. M., Bulut, S., Çağlar M. and Yağmur, N., Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27 (5), (2013) 831-842.
• H. M. Srivastava, S. Gaboury and F. Ghanim, Coefficient estimates for some general subclasses of analytic and bi-univalent functions, Afr. Mat. 28, (2017) 693-706.
• Srivastava, H. M., Gaboury S. and Ghanim, F., Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed. 36, (2016) 863-871.
• Srivastava, H. M., Joshi, B. S., Joshi S. and Pawar, H., Coefficient estimates for certain subclasses of meromorphically bi-univalent functions, Palest. J. Math. 5, (2016) Special Issue, 250-258.
• Srivastava, H. M., Sumer Eker S. and Rosihan Ali, M., Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat 29, (2015) 1839-1845.
• Srivastava H. M. and Bansal, D., Coefficient estimates for a subclass of analytic and bi-univalent functions, J. Egyptian Math. Soc. 23, (2015) 242-246.
• Srivastava, H. M., Gaboury S. and Ghanim, F., Coefficient estimates for some subclasses of M-fold symmetric bi-univalent functions, Acta Univ. Apulensis Math. Inform. 23, (2015) 153-164.
• Srivastava, H. M., Sivasubramanian S. and Sivakumar, R., Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 7, (2014) 1-10.
• Tang, Huo, Srivastava, H. M., Sivasubramanian S. and Gurusamy, P., The Fekete-Szego functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal. 10, (2016) 1063-1092.
• Q.- H. Xu, Y.- C. Gui and H. M. Srivastava, Coefficient estimates for a Certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25, (2012) 990-994.
• Xu, Q. -H., Xiao H. -G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (23), (2012), 11461-11465.
• Z : Zireh A. and Analouei Audegani, E., Coefficient estimates for a subclass of analytic and bi-univalent functions, Bull. Iranian Math. Soc. 42 (2016), 881-889.form [eqref]\eqref{m1.1}. Then