Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1154.30020
Bulboacă, Teodor
Sandwich-type theorems for a class of integral operators.
(English)
[J] Bull. Belg. Math. Soc. - Simon Stevin 13, No. 3, 537-550 (2006). ISSN 1370-1444

Let $H(U)$ be the space of analytic functions of the unit disk $U$. By $f \prec g$ subordination is denoted, i.e. $f = g \circ \omega$ with $\vert \omega\vert < 1$ and $\omega(0) = 0.$ For a given function $h \in H(U)$ the authors define the integral operator $I_{h;\beta} : K \rightarrow H(U),$ with $K \subset H(U),$ by $$I_{h;\beta}[f](z) = \left[\beta \int^z_0 f^{\beta} (t)h^{-1}(t)h'(t) \, dt \right]^{1/\beta} ,$$ where $\beta \in {\Bbb C}$ and all powers are the principal ones. The authors determine sufficient conditions on $g_1, g_2$ and $\beta$ such that $$\left[zh'(z) \over h(z) \right]^{1/ \beta} g_1(z) \prec \left[zh'(z) \over h(z) \right]^{1/ \beta} f(z) \prec \left[zh'(z) \over h(z) \right]^{1/ \beta} g_2(z)$$ implies $$I_{h; \beta}[g_1](z) \prec I_{h; \beta}[f](z) \prec I_{h; \beta} [g_2] (z).$$
[Wolfram Koepf (Kassel)]
MSC 2000:
*30C80 Maximum principle, etc. (one complex variable)
30C45 Special classes of univalent and multivalent functions
45P05 Integral operators

Keywords: univalent functions; differential subordination

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences