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Argument inequalities for certain analytic functions. (English) Zbl 1205.30014

Summary: Let q be analytic in the open unit disk U with q(0)=1 and q(z)0 zU. By using the method of differential subordinations, we derive certain conditions involving q and zq ' under which the functions q satisfy the following two-sided inequality:

-α 2 π 2< arg q(z)<-α 1 π 2(zU)

for some α 1 and α 2 (0<α 1 ,α 2 1. Several interesting consequences of the main results are also given. All these results presented here are sharp.

MSC:
30C45Special classes of univalent and multivalent functions
References:
[1]Brannan, D. A.; Kirwan, W. E.: On some classes of bounded univalent functions, J. London math. Soc. 1, No. 2, 431-443 (1969) · Zbl 0177.33403 · doi:10.1112/jlms/s2-1.1.431
[2]Liu, J. -L.: The Noor integral operator and strongly starlike functions, J. math. Anal. appl. 261, 441-447 (2001) · Zbl 1040.30005 · doi:10.1006/jmaa.2001.7489
[3]Nunokawa, M.: On the order of strongly starlikeness of strongly convex functions, Proc. Japan acad. Ser. A 69, 234-237 (1993) · Zbl 0793.30007 · doi:10.3792/pjaa.69.234
[4]Nunokawa, M.; Owa, S.; Saitoh, H.; Ikeda, A.; Koike, N.: Some results for strongly starlike functions, J. math. Anal. appl. 212, 98-106 (1997) · Zbl 0880.30012 · doi:10.1006/jmaa.1997.5468
[5]Nunokawa, M.; Thomas, D. K.: On convex and starlike functions in a sector, J. aust. Math. soc. Ser. A 60, 363-368 (1996) · Zbl 0864.30008
[6]Obradović, M.; Owa, S.: Some sufficient conditions for strongly starlikeness, Int. J. Math. math. Sci. 24, 643-647 (2000) · Zbl 0980.30012 · doi:10.1155/S0161171200004154
[7]Padmanabhan, K. S.: On sufficient conditions for starlikeness, Indian J. Pure appl. Math. 32, 543-550 (2001) · Zbl 0979.30007
[8]Ponnusamy, S.; Singh, V.: Criteria for strongly starlike functions, Complex variables theory appl. 34, 267-291 (1997) · Zbl 0892.30005
[9]Srivastava, H. M.; Yang, Ding-Gong; Xu, N-Eng: Subordinations for multivalent analytic functions associated with the dziok–Srivastava operator, Integral transforms spec. Funct. 20, 581-606 (2009) · Zbl 1170.30006 · doi:10.1080/10652460902723655
[10]Xu, N-Eng; Yang, Ding-Gong: An application of differential subordinations and some criteria for starlikeness, Indian J. Pure appl. Math. 36, 541-556 (2005) · Zbl 1147.30303
[11]Miller, S. S.; Mocanu, P. T.: Differential subordinations: theory and applications, Series in pure and applied mathematics 225 (2000) · Zbl 0954.34003
[12]Takahashi, N.; Nunokawa, M.: A certain connection between starlike and convex functions, Appl. math. Lett. 16, 653-655 (2003) · Zbl 1064.30008 · doi:10.1016/S0893-9659(03)00062-4