Acta mathematica scientia, Series B >
ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS
Received date: 2012-08-20
Revised date: 2013-03-30
Online published: 2014-01-20
Supported by
The first author is supported by NSFC (11071058) and by Educational Commission of Hubei Province of China (D2011006).
In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors.
Key words: coefficient; univalent function; bi-univalent function; subordination
PENG Zhi-Gang , HAN Qiu-Qiu . ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS[J]. Acta mathematica scientia, Series B, 2014 , 34(1) : 228 -240 . DOI: 10.1016/S0252-9602(13)60140-X
[1] Mocanu P T. Une propriete de convexite generalisee dans la theorie de la representation conforme. Math-ematica (Cluj), 1969, 11: 127–133
[2] Miller S S, Mocanu P T, Reade M O. All -convex functions are univalent and starlike. Proc Amer Math Soc, 1973, 37: 553–554
[3] Lewandowski Z, Miller S, Zlotkiewicz E. Gamma-starlike functions. Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia, 1974, 28: 53–58
[4] Sokol J. On a condition for -starlikeness. J Math Anal Appl, 2009, 352: 696–701
[5] Aouf M K, Dziok J, Sokol J. On a subclass of strongly starlike functions. Appl Math Lett, 2011, 24: 27–32
[6] Sokol J. A certain class of starlike functions. Comput Math Appl, 2011, 62: 611–619
[7] Ali R M. Coefficients of the inverse of strongly starlike functions. Bull Malaysian Math Sci Soc, 2003, 26: 63–71
[8] Ma W C, Minda D. A unified treatment of some special classes of univalent functions//Proceedings of the Conference on Complex Analysis (Tianjin, 1992). Conf Proc Lecture Notes Anal I. Cambridge, MA: Int Press, 1994: 157–169
[9] Badghaish A O, Ali R M, Ravichandran V. Closure properties of operators on the Ma-Minda type starlike and convex functions. Appl Math Comp, 2011, 218: 667–672
[10] Duren P L. Univalent Functions. New York: Springer-Verlag, 1983
[11] Lewin M. On a coefficient problem for bi-univalent functions. Proc Amer Math Soc, 1967, 18: 63–68
[12] Brannan D A, Clunie J G. Aspects of Contemporary Complex Analysis (Proceedings of the NATO Ad-vanced Study Instute Held at the University of Durham, Durham: July 1-20, 1979). New York: Academic Press, 1980
[13] Netanyahu E. The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1. Arch Rational Mech Anal, 1969, 32: 100–112
[14] Brannan D A, Taha T S. On some classes of bi-univalent functions. Studia Univ Babes-Bolyai Math, 1986, 31(2): 70–77
[15] Xu Q H, Gui Y C, Srivastava H M. Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Appl Math Lett, 2012, 25: 990–994
[16] Srivastava H M, Mishra A K, Gochhayat P. Certain subclasses of analytic and bi-univalent functions. Appl Math Lett, 2010, 23: 1188–1192
[17] Frasin B A., Aouf M K. New subclasses of bi-univalent functions. Appl Math Lett, 2011, 24: 1569–1573
[18] Ali R M, Lee S K, Ravichandran V. Shamani Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions. Appl Math Lett, 2012, 25: 344–351
/
| 〈 |
|
〉 |