#### Glasnik Matematicki, Vol. 34, No.1 (1999), 11-18.

### A SPECIAL CLASS OF UNIVALENT OPERATORS

### Teodor Bulboaca

Faculty of Mathematics and Computer Science, Babes-Bolyai
University, 3400 Cluj-Napoca, Romania

*e-mail:* `bulboaca@math.ubbcluj.ro`

**Abstract.** Let *H*(*U*) be the space
of analytic functions in the unit disk *U* and let
*h* ∈ *H*(*U*).
We define a subset
K_{(β,γ),h}
⊂ *H*(*U*) and an integral operator
A_{(β,γ),h} :
K_{(β,γ),h}
→
*H*(*U*). Then we determine a class of functions
whose images by
A_{(β,γ),h}
operators are univalent. In addition, we give some particular cases
of our main result obtained for appropriate choices of
*h*, β and γ.

**1991 Mathematics Subject Classification.**
30C80, 30C45, 30E20.

**Key words and phrases.** Integral operators, univalent
function, differential subordination, subordination chain,
starlike function.

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