ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30, 47 Bulboacă, Teodor, Babeş-Bolyai University, Cluj-Napoca, Romania Differential subordinations and univalent integral operators Let H(U) be the space of analytic functions in the unit disk U and let h ∈ A ⊂ H(U). We define the operator A_{(β,γ),h} : K_{(β,γ),h} ⟶ H(U), K_{(β,γ),h} ⊂

H(U), by A_{(β,γ),h}(f)(z) = [\frac{β+γ}{h^{γ}(z)} ∫_{0}^{z} f^{β}(t) h^{γ−1}(t) h′(t)dt]^{1/β}. We proved that under different assumptions on h, the images of alpha- convex functions by the above operator are still in the same class. Then we determined the images of Bazilevič functions and, in particular, we obtained conditions such that the operator is close-to-convexity preserving. We introduced a class of analytic functions, called strongly close-to-convex functions, and we proved that their images are Bazilevič functions. Finally, we found simple conditions on h such that the images A_{(β,γ),h}(K_{(β,γ),h}) are univalent functions. References: T. Bulboacă, A class of integral operators for alpha-convex functions, Mathematica (Cluj),38(61),1-2(1996),27-33 T. Bulboacă, Classes of integral operators on Bazilevič functions, /to appear/