Proceedings of the Japan Academy, Series A, Mathematical Sciences

Argument estimates for certain analytic functions

Mamoru Nunokawa, Shigeyoshi Owa, Nicolae N. Pascu, and Hitoshi Saitoh

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Let $p(z)$ be analytic in the open unit disk $\mathbf{U}$ with $p(0) = 1$ and $p'(0) = 0$. S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 276 (2002)) have shown some interesting subordination theorems for such functions $p(z)$. The object of the present paper is to discuss some sufficient conditions for arguments of $p(z)$ to be $|\arg p(z)| < (\pi/2) \rho$ for $z \in \mathbf{U}$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 10 (2003), 163-166.

First available in Project Euclid: 18 May 2005

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Zentralblatt MATH identifier

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Analytic function argument estimate subordination


Nunokawa, Mamoru; Owa, Shigeyoshi; Saitoh, Hitoshi; Pascu, Nicolae N. Argument estimates for certain analytic functions. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 10, 163--166. doi:10.3792/pjaa.79.163.

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  • Fukui, S., and Sakaguchi, K.: An extension of a theorem of S. Ruscheweyh. Bull. Fac. Ed. Wakayama Univ. Natur. Sci., 29, 1–3 (1980).
  • Hallenbeck, D. J., and Ruscheweyh, S.: Subordinations by convex functions. Proc. Amer. Math. Soc., 52, 191–195 (1975).
  • Miller, S. S., and Mocanu, P. T.: Libera transform of functions with bounded turning. J. Math. Anal. Appl., 276, 90–97 (2002).
  • Nunokawa, M.: On the order of strongly starlikeness of strongly convex functions. Proc. Japan Acad., 69A, 234–237 (1993).