zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Subclasses of univalent functions. (English) Zbl 0531.30009
Complex analysis - Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math. 1013, 362-372 (1983).

[For the entire collection see Zbl 0516.00016.]

This paper is concerned with the classes S n (α)={f: f is holomorphic in the unit disk U, f(0)=f ' (0)-1=0 and Re[D n+1 f(z)/D n f(z)]>α for zU}, 0α<1, where D 0 f(z)=f(z),D 1 f(z)=Df(z)=zf ' (z) and D n f(z)=D(D n-1 f(z)), n2. Using subordination techniques the sharp result is obtaind that S n+1 (α)S n (δ(α)),0α<1, where δ(α)=(2α-1)/[2(1-2 1-2α )],α1 2, and δ(α)=1/(2ln2),α=1 2· From a corollary it is noted that for 0α<1, all functions in S n (α) are starlike for n a nonnegative integer and convex for n a positive integer. The author also obtains coefficients bounds that generalize a result of H. Silverman and E. M. Silvia [Rocky Mt. J. Math. 10, 469-474 (1980; Zbl 0455.30011)].

Reviewer: D.V.V.Wend

MSC:
30C45Special classes of univalent and multivalent functions
30C50Coefficient problems for univalent and multivalent functions
30C80Maximum principle; Schwarz’s lemma, Lindelöf principle, etc. (one complex variable)