Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1211.30032
Tuneski, Nikola
Convex functions and functions with bounded turning. (English)
[J] Tamsui Oxf. J. Math. Sci. 26, No. 2, 161-172 (2010). ISSN 1561-8307

Summary: Let $\Cal A$ be the class of analytic functions in the unit disk $\Cal U=\{z:\vert z\vert<1\}$ that are normalized by $f(0)=f'(0)-1=0$, and let $-1\le B<A\le 1$ and $-1\le D<C\le 1$. In this paper, the following generalizations of the class of convex functions and of the class of functions with bounded turning are studied: $$ K[A,B]=\bigg\{f\in\Cal A: 1+\frac{zf''(z)}{f'(z)}\prec\frac{1+Az}{1+Bz}\bigg\} $$ and $$ R_k^{}[C,D]=\bigg\{f\in\Cal A: \big(f'(z)\big)^{1/k}\prec\frac{1+Cz}{1+Cz}\bigg\},\qquad k\ge 1. $$Conditions for $K[A,B]\subset R_k[D,D]$ are given, together with several corollaries for different choices of $A$, $B$, $C$, $D$, and $k$,.

MSC 2000:: *30C45 Special classes of univalent and multivalent functions

Keywords: convex function, differential subordination

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]