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Double Subordination-Preserving Properties for Certain Integral Operators
Journal of Inequalities and Applications volume 2007, Article number: 083073 (2007)
Abstract
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.
References
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.
Srivastava HM, Owa S (Eds): Current Topics in Analytic Function Theory. World Scientific, River Edge, NJ, USA; 1992:xiv+456.
Miller SS, Mocanu PT: Subordinants of differential superordinations. Complex Variables. Theory and Application 2003,48(10):815–826. 10.1080/02781070310001599322
Bernardi SD: Convex and starlike univalent functions. Transactions of the American Mathematical Society 1969, 135: 429–446.
Bulboacă T: A class of superordination-preserving integral operators. Indagationes Mathematicae. New Series 2002,13(3):301–311. 10.1016/S0019-3577(02)80013-1
Libera RJ: Some classes of regular univalent functions. Proceedings of the American Mathematical Society 1965,16(4):755–758. 10.1090/S0002-9939-1965-0178131-2
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-L
Miller SS, Mocanu PT, Reade MO: Starlike integral operators. Pacific Journal of Mathematics 1978,79(1):157–168.
Miller SS, Mocanu PT, Reade MO: Subordination-preserving integral operators. Transactions of the American Mathematical Society 1984,283(2):605–615. 10.1090/S0002-9947-1984-0737887-4
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)90082-8
Owa S, Srivastava HM: Univalent and starlike generalized hypergeometric functions. Canadian Journal of Mathematics 1987,39(5):1057–1077. 10.4153/CJM-1987-054-3
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.
Mocanu PT, Ripeanu D, Şerb I: The order of starlikeness of certain integral operators. Mathematica (Cluj) 1981,23(46)(2):225–230.
Pommerenke C: Univalent Functions. Vandenhoeck & Ruprecht, Göttingen, Germany; 1975:376.
Kaplan W: Close-to-convex schlicht functions. The Michigan Mathematical Journal 1952,1(2):169–185.
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Cho, N.E., Owa, S. Double Subordination-Preserving Properties for Certain Integral Operators. J Inequal Appl 2007, 083073 (2007). https://doi.org/10.1155/2007/83073
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DOI: https://doi.org/10.1155/2007/83073