Hokkaido Mathematical Journal

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

Horiana OVESEA-TUDOR and Shigeyoshi OWA

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766285

Digital Object Identifier
doi:10.14492/hokmj/1285766285

Mathematical Reviews number (MathSciNet)
MR2186821

Zentralblatt MATH identifier
1109.30017

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

Keywords
univalent function Löwner chain Nehari criterion Ozaki criterion

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


Export citation