Browse > Article
http://dx.doi.org/10.4134/CKMS.c160063

STARLIKENESS AND SCHWARZIAN DERIVATIVES OF HIGHER ORDER OF ANALYTIC FUNCTIONS  

Kwon, Ohsang (Department of Mathematics Kyungsung University)
Sim, Youngjae (Department of Mathematics Kyungsung University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.1, 2017 , pp. 93-106 More about this Journal
Abstract
In this paper we apply the third-order differential subordination results to normalized analytic functions in the open unit disk. We obtain appropriate classes of admissible functions and find some sufficient conditions of functions to be starlike associated with Tamanoi's Schwarzian derivative of third order. Several interesting examples are also discussed.
Keywords
analytic functions; differential subordination; admissible functions; Schwarzian derivatives; starlike functions;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Owa and M. Obradovic, An application of differential subordinations and some criteria for univalency, Bull. Aust. Math. Soc. 41 (1990), no. 3, 487-494.   DOI
2 E. Schippers, Distortion theorems for higher order Schwarzian derivatives of univalent functions, Proc. Amer. Math. Soc. 128 (2000), no. 11, 3241-3249.   DOI
3 H. Tamanoi, Higher Schwarzian operators and combinatorics of the Schwarzian derivative, Math. Ann. 305 (1996), no. 1, 127-151.   DOI
4 D. Aharonov, A necessary and sufficient condition for univalence of a meromorphic function, Duke Math. J. 36 (1969), 599-604.   DOI
5 R. M. Ali, V. Ravichandran, and N. Seenivasagan, Subordination and superordination on Schwarzian derivatives, J. Inequal. Appl. 2008 (2008), Article ID 712328, 18 pp.
6 A. A. Antonino and S. S. Miller, Third-order differential inequalities and subordinations in the complex plane, Complex Var. Elliptic Equ. 56 (2011), no. 5, 439-454.   DOI
7 R. Harmelin, Aharonov invariants and univalent functions, Israel J. Math. 43 (1982), no. 3, 244-254.   DOI
8 M. P. Jeyaraman and T. K. Suresh, Third-order differential subordination of analytic functions, Acta Univ. Apulensis Math. Inform. 35 (2013), 187-202.
9 S. A. Kim and T. Sugawa, Invariant Schwarzian derivatives of higher order, Complex Anal. Oper. Theory 5 (2011), no. 3, 659-670.   DOI
10 S. S. Miller and P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), no. 2, 289-305.   DOI
11 S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Marcel Dekker, New York, 2000.
12 Z. Nehari, The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc. 55 (1949), 545-551.   DOI
13 Z. Nehari, Some criteria of univalence, Proc. Amer. Math. Soc. 5 (1954), 700-704.   DOI