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)
A unified presentation of some classes of meromorphically multivalent functions. (English) Zbl 0978.30011
Summary: The authors introduce and investigate various properties of a general class $${\cal U}_k[p, \alpha, \beta, A,B],$$ $$(p, k\in\bbfN:= \{1,2,3,\dots,\};\quad 0\le\alpha< p;\quad \beta\ge 0;\quad -1\le A< B\le 1;\quad 0< B\le 1),$$ which unifies and extends several (known or new) subclasses of meromorphically multivalent functions. The properties and characteristics of this general class, which are presented here, include growth and distortion theorems; they also involve Hadamard products (or convolution) of functions belonging to the class ${\cal U}_k[p, \alpha,\beta, A,B]$.

MSC:
30C45Special classes of univalent and multivalent functions
WorldCat.org
Full Text: DOI
References:
[1] Kulkarni, S. R.; Naik, U. H.; Srivastava, H. M.: A certain class of meromorphically p-valent quasi-convex functions. Pan amer. Math. J. 8, No. 1, 57-64 (1998) · Zbl 0957.30013
[2] Owa, S.; Nunokawa, M.; Srivastava, H. M.: A certain class of multivalent functions. Appl. math. Lett. 10, No. 2, 7-10 (1997) · Zbl 0895.30010
[3] Srivastava, H. M.; Owa, S.: Current topics in analytic function theory. (1992) · Zbl 0976.00007
[4] Aouf, M. K.: A generalization of meromorphic multivalent functions with positive coefficients. Math. japon. 35, 609-614 (1990) · Zbl 0714.30020
[5] Mogra, M. L.: Meromorphic multivalent functions with positive coefficients, I. Math. japon. 35, 1-11 (1990) · Zbl 0705.30019
[6] Miller, J. E.: Convex meromorphic mappings and related functions. Proc. amer. Math. soc. 25, 220-228 (1970) · Zbl 0196.09202
[7] Pommerenke, Ch.: On meromorphic starlike functions. Pacific J. Math. 13, 221-235 (1963) · Zbl 0116.05701
[8] Clunie, J.: On meromorphic schlicht functions. J. London math. Soc. 34, 215-216 (1959) · Zbl 0087.07704
[9] Royster, W. C.: Meromorphic starlike multivalent functions. Trans. amer. Math. soc. 107, 300-308 (1963) · Zbl 0112.05101
[10] Mogra, M. L.: Meromorphic multivalent functions with positive coefficients, II. Math. japon. 35, 1089-1098 (1990) · Zbl 0718.30009
[11] Aouf, M. K.: On a class of meromorphic multivalent functions with positive coefficients. Math. japon. 35, 603-608 (1990) · Zbl 0715.30013
[12] Uralegaddi, B. A.; Ganigi, M. D.: Meromorphic multivalent functions with positive coefficients. Nepali math. Sci. rep. 11, 95-102 (1986) · Zbl 0656.30011