Banach Journal of Mathematical Analysis

On a class of univalent functions defined by Salagean differential operator

Georgia Irina Oros, Roxana Sendrutiu, and Adela Olimpia Taut

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Abstract

By using a certain operator $S^n$, we introduce a class of holomorphic functions $S_n(\beta )$, and obtain some subordination results. We also show that the set $S_n(\beta )$ is convex and obtain some new differential subordinations related to certain integral operators.

Article information

Source
Banach J. Math. Anal. Volume 3, Number 1 (2009), 61-67.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
http://projecteuclid.org/euclid.bjma/1240336424

Mathematical Reviews number (MathSciNet)
MR2461747

Zentralblatt MATH identifier
1155.30339

Digital Object Identifier
doi:10.15352/bjma/1240336424

Subjects
Primary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30A20 34A40: Differential inequalities [See also 26D20]

Keywords
differential operator differential subordination dominant best dominant

Citation

Taut, Adela Olimpia; Oros, Georgia Irina; Sendrutiu, Roxana. On a class of univalent functions defined by Salagean differential operator. Banach Journal of Mathematical Analysis 3 (2009), no. 1, 61--67. doi:10.15352/bjma/1240336424. http://projecteuclid.org/euclid.bjma/1240336424.


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References

  • G. Oros and G.I. Oros, A Class of Holomorphic Function II, Libertas Math., 23 (2003), 65–-68.
  • G.S. Sălăgean, Subclasses of univalent functions, Complex Analysis–Fift Romanian–Finnish Seminar, Part 1 (Bucharest, 1981), 362–372, Lecture Notes in Math., 1013, Springer, Berlin 1983.
  • D.J. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc., 52 (1975), 191–195.