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)
Sandwich-type theorems for multivalent functions associated with the Srivastava-Attiya operator. (English) Zbl 1202.30017
Summary: We investigate some subordination- and superordination-preserving properties for certain classes of multivalent analytic functions in the open unit disk, which are associated with such multiplier transformations as the Srivastava-Attiya operator. Various sandwich-type theorems for functions belonging to these classes are also obtained.

30C45Special classes of univalent and multivalent functions
Full Text: DOI
[1] Bernardi, S. D.: Convex and starlike univalent functions, Trans. amer. Math. soc. 135, 429-446 (1969) · Zbl 0172.09703 · doi:10.2307/1995025
[2] Bulboacă, T.: Integral operators that preserve the subordination, Bull. korean math. Soc. 32, 627-636 (1997) · Zbl 0898.30021
[3] Bulboacă, T.: A class of superordination-preserving integral operators, Indag. math. (New ser.) 13, 301-311 (2002) · Zbl 1019.30023 · doi:10.1016/S0019-3577(02)80013-1
[4] Cho, N. E.; Srivastava, H. M.: Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. comput. Modelling 37, 39-49 (2003) · Zbl 1050.30007 · doi:10.1016/S0895-7177(03)80004-3
[5] Cho, N. E.; Srivastava, H. M.: A class of nonlinear integral operators preserving subordination and superordination, Integral transforms spec. Funct. 18, 95-107 (2007) · Zbl 1109.30022 · doi:10.1080/10652460601135342
[6] Cho, N. E.; Kwon, O. S.; Owa, S.; Srivastava, H. M.: A class of integral operators preserving subordination and superordination for meromorphic functions, Appl. math. Comput. 193, 463-474 (2007) · Zbl 1193.30032 · doi:10.1016/j.amc.2007.03.084
[7] Goel, R. M.; Sohi, N. S.: A new criterion for p-valent functions, Proc. amer. Math. soc. 78, 353-357 (1980) · Zbl 0444.30012 · doi:10.2307/2042324
[8] Jung, I. B.; Kim, Y. C.; Srivastava, H. M.: The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. math. Anal. appl. 176, 138-147 (1993) · Zbl 0774.30008 · doi:10.1006/jmaa.1993.1204
[9] Kaplan, W.: Close-to-convex schlicht functions, Michigan math. J. 2, 169-185 (1952) · Zbl 0048.31101 · doi:10.1307/mmj/1028988895
[10] Libera, R. J.: Some classes of regular univalent functions, Proc. amer. Math. soc. 16, 755-758 (1965) · Zbl 0158.07702 · doi:10.2307/2033917
[11] Miller, S. S.; Mocanu, P. T.: Differential subordinations and univalent functions, Michigan math. J. 28, 157-171 (1981) · Zbl 0439.30015 · doi:10.1307/mmj/1029002507
[12] Miller, S. S.; Mocanu, P. T.: Univalent solutions of briot -- bouquet differential equations, J. differential equations 567, 297-309 (1985) · Zbl 0507.34009 · doi:10.1016/0022-0396(85)90082-8
[13] Miller, S. S.; Mocanu, P. T.: Differential subordination: theory and applications, Vol. 225 225 (2000) · Zbl 0954.34003
[14] Miller, S. S.; Mocanu, P. T.: Subordinants of differential superordinations, Complex variables theory appl. 48, 815-826 (2003) · Zbl 1039.30011 · doi:10.1080/02781070310001599322
[15] Miller, S. S.; Mocanu, P. T.; Reade, M. O.: Subordination-preserving integral operators, Trans. amer. Math. soc. 283, 605-615 (1984) · Zbl 0506.30011 · doi:10.2307/1999149
[16] Owa, S.; Srivastava, H. M.: Some applications of the generalized libera integral operator, Proc. Japan acad. Ser. A math. Sci. 62, 125-128 (1986) · Zbl 0583.30016 · doi:10.3792/pjaa.62.125
[17] Owa, S.; Srivastava, H. M.: Some subordination theorems involving a certain family of integral operators, Integral transforms spec. Funct. 15, 445-454 (2004) · Zbl 1057.30015 · doi:10.1080/10652460410001686046
[18] Pommerenke, Ch.: Univalent functions, (1975)
[19] Prajapat, J. K.; Goyal, S. P.: Applications of Srivastava -- attiya operator to the class of strongly starlike and strongly convex functions, J. math. Inequal. 3, 129-137 (2009) · Zbl 1160.30325 · http://files.ele-math.com/abstracts/jmi-03-13-abs.pdf
[20] &scedil, G.; Sălăgean, .: Subclasses of univalent functions, Lecture notes in mathematics 1013, 362-372 (1983)
[21] Srivastava, H. M.; Attiya, A. A.: An integral operator associated with the Hurwitz -- lerch zeta function and differential subordination, Integral transforms spec. Funct. 18, 207-216 (2007) · Zbl 1112.30007 · doi:10.1080/10652460701208577
[22] , Current topics in analytic function theory (1992)
[23] Uralegaddi, B. A.; Somanatha, C.: Certain classes of univalent functions, Current topics in analytic function theory, 371-374 (1992) · Zbl 0987.30508
[24] Wang, Z. -G.; Li, Q. -G.; Jiang, Y. -P.: Certain subclasses of multivalent analytic functions involving the generalized Srivastava -- attiya operator, Integral transforms spec. Funct. 21, 221-234 (2010) · Zbl 1187.30024 · doi:10.1080/10652460903098248