A Class of Nonlinear Integral Operators Preserving Double Subordinations
Oh Sang Kwon and Nak Eun Cho
Source: Abstr. Appl. Anal. Volume 2008 (2008), 10 pages.
Abstract
The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain integral operators defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also considered.
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969169
Digital Object Identifier: doi:10.1155/2008/792160
Mathematical Reviews number (MathSciNet):
MR2407282
Zentralblatt MATH identifier:
1152.30311
References
S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, vol. 225 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000.
Mathematical Reviews (MathSciNet):
MR1760285
Zentralblatt MATH:
0954.34003
A. W. Goodman, Univalent Functions. Vol. II, Mariner, Tampa, Fla, USA, 1983.
Mathematical Reviews (MathSciNet):
MR0704184
Zentralblatt MATH:
1041.30501
S. S. Miller and P. T. Mocanu, ``Univalent solutions of Briot-Bouquet differential equations,'' Journal of Differential Equations, vol. 56, no. 3, pp. 297--309, 1985.
Mathematical Reviews (MathSciNet):
MR780494
Zentralblatt MATH:
0507.34009
Digital Object Identifier: doi:10.1016/0022-0396(85)90082-8
S. K. Bajpai, ``A note on a class of meromorphic univalent functions,'' Revue Roumaine de Mathématiques Pures et Appliquées, vol. 22, no. 3, pp. 295--297, 1977.
Mathematical Reviews (MathSciNet):
MR0447546
Zentralblatt MATH:
0354.30006
S. S. Bhoosnurmath and S. R. Swamy, ``Certain integrals for classes of univalent meromorphic functions,'' Ganita, vol. 44, no. 1-2, pp. 19--25, 1993.
Mathematical Reviews (MathSciNet):
MR1257708
Zentralblatt MATH:
0833.30006
A. Dernek, ``Certain classes of meromorphic functions,'' Annales Universitatis Mariae Curie-Skłodowska. Sectio A, vol. 42, pp. 1--8, 1988.
Mathematical Reviews (MathSciNet):
MR1074838
Zentralblatt MATH:
0714.30019
S. P. Dwivedi, G. P. Bhargava, and S. L. Shukla, ``On some classes of meromorphic univalent functions,'' Revue Roumaine de Mathématiques Pures et Appliquées, vol. 25, no. 2, pp. 209--215, 1980.
Mathematical Reviews (MathSciNet):
MR577028
Zentralblatt MATH:
0439.30007
R. M. Goel and N. S. Sohi, ``On a class of meromorphic functions,'' Glasnik Matematički, vol. 17(37), no. 1, pp. 19--28, 1982.
Mathematical Reviews (MathSciNet):
MR682470
Zentralblatt MATH:
0504.30005
S. Stević, ``The generalized Libera transform on Hardy, Bergman and Bloch spaces on the unit polydisc,'' Zeitschrift für Analysis und ihre Anwendungen, vol. 22, no. 1, pp. 179--186, 2003.
Mathematical Reviews (MathSciNet):
MR1962082
Zentralblatt MATH:
1046.47026
S. Stević, ``A note on the generalized Cesàro operator on Bergman spaces,'' Indian Journal of Mathematics, vol. 46, no. 1, pp. 129--136, 2004.
Mathematical Reviews (MathSciNet):
MR2108180
Zentralblatt MATH:
1088.47025
S. Stević, ``On Libera type transform čommentComment on ref. [18?]: Please update the information of this reference, if possible. on the unit disc, polydisc and the unit ball,'' to appear in Integral Transforms and Special Functions.
S. S. Miller, P. T. Mocanu, and M. O. Reade, ``Subordination-preserving integral operators,'' Transactions of the American Mathematical Society, vol. 283, no. 2, pp. 605--615, 1984.
Mathematical Reviews (MathSciNet):
MR737887
Zentralblatt MATH:
0506.30011
Digital Object Identifier: doi:10.2307/1999149
JSTOR: links.jstor.org
S. Owa and H. M. Srivastava, ``Some subordination theorems involving a certain family of integral operators,'' Integral Transforms and Special Functions, vol. 15, no. 5, pp. 445--454, 2004.
Mathematical Reviews (MathSciNet):
MR2086656
Zentralblatt MATH:
1057.30015
Digital Object Identifier: doi:10.1080/10652460410001727563
T. Bulboacă, ``A class of superordination-preserving integral operators,'' Indagationes Mathematicae. New Series, vol. 13, no. 3, pp. 301--311, 2002.
Mathematical Reviews (MathSciNet):
MR2057051
Zentralblatt MATH:
1019.30023
Digital Object Identifier: doi:10.1016/S0019-3577(02)80013-1
S. S. Miller and P. T. Mocanu, ``Differential subordinations and univalent functions,'' Michigan Mathematical Journal, vol. 28, no. 2, pp. 157--172, 1981.
Mathematical Reviews (MathSciNet):
MR616267
Zentralblatt MATH:
0439.30015
Digital Object Identifier: doi:10.1307/mmj/1029002507
Project Euclid: euclid.mmj/1029002507
Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975.
Mathematical Reviews (MathSciNet):
MR0507768
Zentralblatt MATH:
0298.30014
W. Kaplan, ``Close-to-convex schlicht functions,'' Michigan Mathematical Journal, vol. 1, pp. 169--185, 1952.
Mathematical Reviews (MathSciNet):
MR0054711
Zentralblatt MATH:
0048.31101
Digital Object Identifier: doi:10.1307/mmj/1028988895
Project Euclid: euclid.mmj/1028988895
Abstract and Applied Analysis
