## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Univalency of certain analytic functions

#### Abstract

Let $\mathcal{A}$ be the class of functions $f(z)$ which are analytic in the open unit disk $\mathbf{U}$ with $f(0) = 0$ and $f'(0) = 1$. Using $g(z) \in \mathcal{A}$, the subclass $\mathcal{T}(\lambda, \mu, g)$ of $\mathcal{A}$ consisting of functions $f(z)$ is introduced. The object of the present paper is to consider some univalence conditions for functions $f(z)$ belonging to the class $\mathcal{T}(\lambda, \mu, g)$ applying the subordination properties of analytic functions.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 7 (2002), 148-151.

Dates
First available in Project Euclid: 23 May 2006

https://projecteuclid.org/euclid.pja/1148392639

Digital Object Identifier
doi:10.3792/pjaa.78.148

Mathematical Reviews number (MathSciNet)
MR1930221

Zentralblatt MATH identifier
1032.30010

#### Citation

Yang, Dinggong; Owa, Shigeyoshi. Univalency of certain analytic functions. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 148--151. doi:10.3792/pjaa.78.148. https://projecteuclid.org/euclid.pja/1148392639

#### References

• Duren, P. L.: Univalent Functions. Springer-Verlag, New York (1983).
• Miller, S. S., and Mocanu, P. T.: Differential subordinations and univalent functions. Michigan Math. J., 28, 157–171 (1981).
• Nunokawa, M., Obradović, M., and Owa, S.: One criterion for univalency. Proc. Amer. Math. Soc., 106, 1035–1037 (1989).
• Ozaki, S., and Nunokawa, M.: The Schwarzian derivative and univalent functions. Proc. Amer. Math. Soc., 33, 392–394 (1972).
• Yang, D.: Some criteria for multivalently starlikeness. Southeast Asian Bull. Math., 24, 491–497 (2000).
• Yang, D., and Liu, J.: On a class of univalent functions. Internat. J. Math. Math. Sci., 22, 605–610 (1999).