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http://dx.doi.org/10.5666/KMJ.2019.59.2.215

Coefficient Bounds for Several Subclasses of Analytic and Biunivalent Functions

Rahrovi, Samira (Department of Mathematics, Basic Science Faculty, University of Bonab)
Piri, Hossein (Department of Mathematics, Basic Science Faculty, University of Bonab)
Sokol, Janusz (Faculty of Mathematics and Natural Sciences, University of Rzeszow)

Publication Information

Kyungpook Mathematical Journal / v.59, no.2, 2019 , pp. 215-224 More about this Journal

Abstract

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated.

Keywords

bi-univalent function; starlike function of order ${\alpha}$ ; strongly starlike functions; strongly convex functions of order ${\alpha}$ ; subordination;

Citations & Related Records

Reference

1	M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18(1967), 63-68. DOI
2	S. S. Miller, P. T. Mocanu and M. O. Reade, All ${\alpha}$ -convex functions are univalent and starlike, Proc. Amer. Math. Soc., 37(1973), 553-554. DOI
3	P. T. Mocanu, Une propriete de convexite generalisee dans la theorie de la representation conforme, Mathematica (Cluj), 11(1969), 127-133.
4	E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $\left\|z\right\|<1$, Arch. Rational Mech. Anal., 32(1969), 100-112. DOI
5	S. Rahrovi and H. Piri, Certain subclasses of bi-univalent functions associated with the Komatu operator, Submmited paper.
6	J. Sokol, On a condition for ${\alpha}$ -starlikeness, J. Math. Anal. Appl., 352(2009), 696-701. DOI
7	J. Sokol, A certain class of starlike functions, Comput. Math. Appl., 62(2011), 611-619. DOI
8	H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188-1192. DOI
9	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. DOI
10	R. M. Ali, S. K. Lee, V. Ravichandran and Sh. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett., 25(2012), 344-351. DOI
11	M. K. Aouf, J. Dziok and J. Sokol, On a subclass of strongly starlike functions, Appl. Math. Lett., 24(2011), 27-32. DOI
12	D. A. Brannan and J. G. Clunie, Aspects of Contemporary Complex Analysis, (Proceedings of the NATO Advanced Study Instute Held at the University of Durham, Durham: July 1-20, 1979), Academic Press, New York, 1980.
13	D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math., 31(2)(1986), 70-77.
14	P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
15	B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), 1569-1573. DOI
16	Z. Lewandowski, S. S. Miller and E. Zlotkiewicz, Gamma-starlike functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 28(1974), 53-58.