Taishun LIU
,
Qinghua XU
. FEKETE AND SZEGÖ INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER α ON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN Cn[J]. Acta mathematica scientia, Series B, 2017
, 37(3)
: 722
-731
.
DOI: 10.1016/S0252-9602(17)30033-4
[1] Bieberbach L. Über die Koeffizienten der einigen Potenzreihen welche eine schlichte Abbildung des Einheitskreises vermitten. SB Preuss Akad Wiss, 1916
[2] Bhowmik B, Ponnusamy S, Wirths K J. On the Fekete-Szegö problem for concave univalent functions. J Math Anal Appl, 2011, 373:432-438
[3] Cartan H. Sur la possibilité d'étendre aux fonctions de plusieurs variables complexes la théorie des fonctions univalentes//Montel P. Lecons sur les Fonctions Univalentes ou Multivalentes. Paris:Gauthier-Villars, 1933
[4] de Branges L. A proof of the Bieberbach conjecture. Acta Math, 1985, 154(1/2):137-152
[5] Fekete M, Szegö G. Eine Bemerkunguber ungerade schlichte Funktionen. J Lond Math Soc, 1933, 8:85-89
[6] Gong S. The Bieberbach Conjecture. Providence, RI:Amer Math Soc, International Press, 1999
[7] Graham I, Hamada H, Kohr G. Parametric representation of univalent mappings in several complex variables. Canadian J Math, 2002, 54:324-351
[8] Graham I, Kohr G, Kohr M. Loewner chains and parametric representation in several complex variables. J Math Anal Appl, 2003, 281:425-48
[9] Graham I, Kohr G. Geometric Function Theory in One and Higher Dimensions. New York:Marcel Dekker, 2003
[10] Hamada H, Kohr G, Liczberski P. Starlike mappings of order α on the unit ball in complex Banach spaces. Glas Mat Ser, 2001, 36(3):39-48
[11] Hamada H, Honda T, Kohr G. Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation. J Math Anal Appl, 2006, 317:302-319
[12] Hamada H, Honda T. Sharp growth theorems and coefficient bounds for starlike mappings in several complex variables. Chin Ann Math, 2008, 29B(4):353-368
[13] Kohr G. Certain partial differential inequalities and applications for holomorphic mappings defined on the unit ball of Cn. Ann Univ Mariae Curie Skl, Sect A, 1996, 50:87-94
[14] Kohr G. On some best bounds for coefficients of several subclasses of biholomorphic mappings in Cn. Complex Variables, 1998, 36:261-284
[15] Kanas S. An unified approach to the Fekete-Szegö problem. Appl Math Comput, 2012, 218:8453-8461
[16] Koepf W. On the Fekete-Szegö problem for close-to-convex functions. Proc Am Math Soc, 1987, 101:89-95
[17] Keogh F R, Merkes E P. A coefficient inequality for certain classes of analytic functions. Proc Am Math Soc, 1969, 20:8-12
[18] London P R. Fekete-Szegö inequalities for close-to-convex functions. Proc Am Math Soc, 1993, 117(4):947-950
[19] Liu T S, Ren G B. The growth theorem for starlike mappings on bounded starlike circular domains. Chin Ann of Math, 1998, 19B:401-408
[20] Liu H, Lu K P. Two subclasses of starlike mappings in several complex variables. Chin Ann Math Ser A, 2000, 21(5):533-546
[21] Liu X S, Liu T S. The sharp estimates of all homogeneous expansions for a class of quasi-convex mappings on the unit polydisk in Cn. Chin Ann Math, 2011, 32B:241-252
[22] Pfluger A. The Fekete-Szegö inequality for complex parameter. Complex Var Theory Appl, 1986, 7:149-160
[23] Xu Q H, Liu T S. On coefficient estimates for a class of holomorphic mappings. Sci China Ser A-Math, 2009, 52:677-686
[24] Xu Q H, Liu T S. Biholomorphic mappings on bounded starlike circular domain. J Math Anal Appl, 2010, 366:153-163
[25] Xu Q H, Liu T S, Liu X S. The sharp estimates of homogeneous expansions for the generalized class of close-to-quasi-convex mappings. J Math Anal Appl, 2012, 389:781-791