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)
A new class of meromorphically multivalent functions with applications to generalized hypergeometric functions. (English) Zbl 1140.30007
In this paper the authors define a class of functions $f(z)$ that are meromorphic, normalized, analytic and $p$-valent in the punctured unit disc $U^*$ and satisfy the subordination $$ \gamma\frac{(f*g)^{(m)}(z)}{(f*h)^{(m)}(z)} \prec \gamma -\frac{p(A-B)z}{1+Bz} \quad (z\in U^*),$$ where $\gamma>0,$ $0\le B<A\le 1,$ $b_n\ge c_n\ge0$ $(n\ge p)$, $p\ge m$ $(m\in\{2j-1:j\in \mathbb{N} \}\cup\{0\}),$ provided that $(f*h)^{(m)}(z)\neq 0$ $(z\in U^*).$ Here $b_n$ and $c_n$ are the coefficients of functions $g(z)$ and $h(z),$ respectively, $"*"$ denotes the Hadamard product (convolution) and “$\prec$” denotes subordination. The authors give coefficient estimates, distortion properties and radii of convexity and starlikeness for this class of functions together with some applications of the main result concerning generalized hypergeometric functions. At the end of the paper some remarks for further investigation are given.

30C45Special classes of univalent and multivalent functions
Full Text: DOI
[1] Liu, J. -L.; Srivastava, H. M.: Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. Math. comput. Modelling 39, 21-34 (2004) · Zbl 1049.30008
[2] Liu, J. -L.; Srivastava, H. M.: Subclasses of meromorphically multivalent functions associated with a certain linear operator. Math. comput. Modelling 39, 35-44 (2004) · Zbl 1049.30009
[3] Dziok, J.; Raina, R. K.: Families of analytic functions associated with the wright’s generalized hypergeometric function. Demonstratio math. 37, 533-542 (2004) · Zbl 1058.30014
[4] Dziok, J.; Srivastava, H. M.: Classes of analytic functions associated with the generalized hypergeometric function. Appl. math. Comput. 103, 1-13 (1999) · Zbl 0937.30010
[5] Srivastava, H. M.; Karlsson, P. W.: Multiple Gaussian hypergeometric series. (1985) · Zbl 0552.33001
[6] Dziok, J.; Raina, R. K.; Srivastava, H. M.: Some classes of analytic functions associated with operators on Hilbert space involving wright’s generalized hypergeometric function. Proc. jangjeon math. Soc. 7, 43-55 (2004) · Zbl 1060.30017