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Differential subordinations associated with multiplier transformations. (English) Zbl 1153.30021

Summary: The authors introduce new classes of analytic functions in the open unit disc which are defined by using multiplier transformations. The properties of these classes will be studied by using techniques involving the Briot-Bouquet differential subordinations. Also an integral transform is established.

MSC:

30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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[1] A. C\uata\cs, “Sandwich theorems associated with new multiplier transformations,” submitted. · Zbl 0331.30011
[2] F. M. Al-Oboudi, “On univalent functions defined by a generalized S\ual\uagean operator,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 27, pp. 1429-1436, 2004. · Zbl 1072.30009
[3] G. \cS. S\ual\uagean, “Subclasses of univalent functions,” in Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1, vol. 1013 of Lecture Notes in Mathematics, pp. 362-372, Springer, Berlin, Germany, 1983. · Zbl 0531.30009
[4] N. E. Cho and H. M. Srivastava, “Argument estimates of certain analytic functions defined by a class of multiplier transformations,” Mathematical and Computer Modelling, vol. 37, no. 1-2, pp. 39-49, 2003. · Zbl 1050.30007
[5] N. E. Cho and T. H. Kim, “Multiplier transformations and strongly close-to-convex functions,” Bulletin of the Korean Mathematical Society, vol. 40, no. 3, pp. 399-410, 2003. · Zbl 0331.30011
[6] B. A. Uralegaddi and C. Somanatha, “Certain classes of univalent functions,” in Current Topics in Analytic Function Theory, pp. 371-374, World Scientific, River Edge, NJ, USA, 1992. · Zbl 0331.30011
[7] M. Acu and S. Owa, “Note on a class of starlike functions,” in Proceeding of the International Short Joint Work on Study on Calculus Operators in Univalent Function Theory, pp. 1-10, RIMS, Kyoto, Japan, August 2006. · Zbl 0331.30011
[8] S. Sivaprasad Kumar, H. C. Taneja, and V. Ravichandran, “Classes of multivalent functions defined by Dziok-Srivastava linear operator and multiplier transformation,” Kyungpook Mathematical Journal, vol. 46, no. 1, pp. 97-109, 2006. · Zbl 0331.30011
[9] E. T. Whittaker and G. N. Watson, 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, Cambridge University Press, Cambridge, UK, 4 edition, 1927. · Zbl 0331.30011
[10] P. Eenigenburg, S. S. Miller, P. T. Mocanu, and M. O. Reade, “On a Briot-Bouquet differential subordination,” in General Inequalities 3, vol. 64 of Internationale Schriftenreihe Numerische Mathematik, pp. 339-348, Birkhäuser, Basel, Switzerland, 1983. · Zbl 0331.30011
[11] D. R. Wilken and J. Feng, “A remark on convex and starlike functions,” Journal of the London Mathematical Society. Second Series, vol. 21, no. 2, pp. 287-290, 1980. · Zbl 0331.30011
[12] S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Application, vol. 225 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000. · Zbl 0331.30011
[13] J. Patel, “Inclusion relations and convolution properties of certain subclasses of analytic functions defined by generalized S\ual\uagean operator,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 15, no. 1, pp. 33-47, 2008. · Zbl 0331.30011
[14] J. Patel, N. E. Cho, and H. M. Srivastava, “Certain subclasses of multivalent functions associated with a family of linear operators,” Mathematical and Computer Modelling, vol. 43, no. 3-4, pp. 320-338, 2006. · Zbl 1138.30010
[15] T. H. MacGregor, “A subordination for convex functions of order \alpha ,” Journal of the London Mathematical Society, vol. 9, no. 4, pp. 530-536, 1975. · Zbl 0331.30011
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