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Some applications of a subordination theorem for a class of analytic functions. (English) Zbl 1138.30014

Summary: By making use of a subordination theorem for analytic functions, we derive several subordination relationships between certain subclasses of analytic functions which are defined by means of the Sălăgean derivative operator. Some interesting corollaries and consequences of our results are also considered.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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References:

[1] S.S. Eker, S. Owa, Certain classes of analytic functions involving Sălăgean operator, J. Inequal. Pure Appl. Math. (in course of publication); S.S. Eker, S. Owa, Certain classes of analytic functions involving Sălăgean operator, J. Inequal. Pure Appl. Math. (in course of publication) · Zbl 1165.26325
[2] Gao, C.-Y.; Yuan, S.-M.; Srivastava, H. M., Some functional inequalities and inclusion relationships associated with certain families of integral operators, Comput. Math. Appl., 49, 1787-1795 (2005) · Zbl 1085.30014
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[4] Owa, S.; Nunokawa, M.; Saitoh, H.; Srivastava, H. M., Close-to-convexity, starlikeness, and convexity of certain analytic functions, Appl. Math. Lett., 15, 63-69 (2002) · Zbl 1038.30011
[5] Sălăgean, G.Ş., Subclasses of univalent functions, (Complex Analysis: Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981). Complex Analysis: Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Mathematics, vol. 1013 (1983), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York), 362-372
[6] Wilf, H. S., Subordinating factor sequences for convex maps of the unit circle, Proc. Amer. Math. Soc., 12, 689-693 (1961) · Zbl 0100.07201
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