Open Access

Double Subordination-Preserving Properties for Certain Integral Operators

Journal of Inequalities and Applications20072007:083073

Received: 27 November 2006

Accepted: 4 January 2007

Published: 11 February 2007


The purpose of the present paper is to obtain the sandwich-type theorem which contains the subordination- and superordination-preserving properties for certain integral operators defined on the space of normalized analytic functions in the open unit disk.


Analytic FunctionIntegral OperatorUnit DiskOpen UnitOpen Unit Disk


Authors’ Affiliations

Department of Applied Mathematics, Pukyong National University, Pusan, South Korea
Department of Mathematics, Kinki University, Osaka, Japan


  1. Miller SS, Mocanu PT: Differential Subordinations: Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 225. Marcel Dekker, New York, NY, USA; 2000:xii+459.Google Scholar
  2. Srivastava HM, Owa S (Eds): Current Topics in Analytic Function Theory. World Scientific, River Edge, NJ, USA; 1992:xiv+456.MATHGoogle Scholar
  3. Miller SS, Mocanu PT: Subordinants of differential superordinations. Complex Variables. Theory and Application 2003,48(10):815–826. 10.1080/02781070310001599322MathSciNetView ArticleMATHGoogle Scholar
  4. Bernardi SD: Convex and starlike univalent functions. Transactions of the American Mathematical Society 1969, 135: 429–446.MathSciNetView ArticleMATHGoogle Scholar
  5. Bulboacă T: A class of superordination-preserving integral operators. Indagationes Mathematicae. New Series 2002,13(3):301–311. 10.1016/S0019-3577(02)80013-1MathSciNetView ArticleMATHGoogle Scholar
  6. Libera RJ: Some classes of regular univalent functions. Proceedings of the American Mathematical Society 1965,16(4):755–758. 10.1090/S0002-9939-1965-0178131-2MathSciNetView ArticleMATHGoogle Scholar
  7. Miller SS, Mocanu PT: Classes of univalent integral operators. Journal of Mathematical Analysis and Applications 1991,157(1):147–165. 10.1016/0022-247X(91)90141-LMathSciNetView ArticleMATHGoogle Scholar
  8. Miller SS, Mocanu PT, Reade MO: Starlike integral operators. Pacific Journal of Mathematics 1978,79(1):157–168.MathSciNetView ArticleGoogle Scholar
  9. Miller SS, Mocanu PT, Reade MO: Subordination-preserving integral operators. Transactions of the American Mathematical Society 1984,283(2):605–615. 10.1090/S0002-9947-1984-0737887-4MathSciNetView ArticleMATHGoogle Scholar
  10. Miller SS, Mocanu PT: Univalent solutions of Briot-Bouquet differential equations. Journal of Differential Equations 1985,56(3):297–309. 10.1016/0022-0396(85)90082-8MathSciNetView ArticleMATHGoogle Scholar
  11. Owa S, Srivastava HM: Univalent and starlike generalized hypergeometric functions. Canadian Journal of Mathematics 1987,39(5):1057–1077. 10.4153/CJM-1987-054-3MathSciNetView ArticleMATHGoogle Scholar
  12. Whittaker ET, Watson GN: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions: With an Account of the Principal Transcendental Functions. 4th edition. Cambridge University Press, Cambridge, UK; 1927.MATHGoogle Scholar
  13. Mocanu PT, Ripeanu D, Şerb I: The order of starlikeness of certain integral operators. Mathematica (Cluj) 1981,23(46)(2):225–230.Google Scholar
  14. Pommerenke C: Univalent Functions. Vandenhoeck & Ruprecht, Göttingen, Germany; 1975:376.MATHGoogle Scholar
  15. Kaplan W: Close-to-convex schlicht functions. The Michigan Mathematical Journal 1952,1(2):169–185.MathSciNetView ArticleMATHGoogle Scholar


© N. E. Cho and S. Owa 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.