## Hokkaido Mathematical Journal

### An extension of the univalence criteria of Nehari and Ozaki and Nunokawa

#### Abstract

In this paper, we obtain a sufficient condition for the univalence of analytic functions in the open unit disk $\mathbb{U}$. This condition involves two arbitrary functions $g(z)$ and $h(z)$ analytic in $\mathbb{U}$. Replacing $g(z)$ and $h(z)$ by some particular functions, we find the well-known conditions for univalency established by Z.Nehari (Bull. Amer. Math. Soc. 55(1949)) and S.Ozaki and M.Nunokawa (Proc. Amer. Math. Sco., 33(1972))}. Likewise we find other new sufficient conditions.

#### Article information

Source
Hokkaido Math. J., Volume 34, Number 3 (2005), 533-539.

Dates
First available in Project Euclid: 29 September 2010

https://projecteuclid.org/euclid.hokmj/1285766285

Digital Object Identifier
doi:10.14492/hokmj/1285766285

Mathematical Reviews number (MathSciNet)
MR2186821

Zentralblatt MATH identifier
1109.30017

#### Citation

OVESEA-TUDOR, Horiana; OWA, Shigeyoshi. An extension of the univalence criteria of Nehari and Ozaki and Nunokawa. Hokkaido Math. J. 34 (2005), no. 3, 533--539. doi:10.14492/hokmj/1285766285. https://projecteuclid.org/euclid.hokmj/1285766285