zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Techniques of the differential subordination for domains bounded by conic sections. (English) Zbl 1130.30307
Summary: We solve the problem of finding the largest domain $D$ for which, under given $\psi$ and $q$, the differential subordination $\psi(p(z), zp^{\prime}(z)) \in D \Rightarrow p(z) \prec q(z)$, where $D$ and $q(\cal{U})$ are regions bounded by conic sections, is satisfied. The shape of the domain $D$ is described by the shape of $q(\cal{U})$. Also, we find the best dominant of the differential subordination $p(z) +({zp^{\prime}(z)}/({\beta p(z) + \gamma})) \prec p_{k}(z)$, when the function $p_k$ $(k\in [0,\infty))$ maps the unit disk onto a conical domain contained in a right half-plane. Various applications in the theory of univalent functions are also given.

30C45Special classes of univalent and multivalent functions
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
33E05Elliptic functions and integrals
30C35General theory of conformal mappings
Full Text: DOI EuDML