Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SOME PROPERTIES OF CERTAIN CLASSES OF FUNCTIONS WITH BOUNDED RADIUS ROTATIONS

  • NOOR, KHALIDA INAYAT (Mathematics Department, College of Science, King Saud University)
  • Received : 1996.06.20
  • Published : 19970000
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Abstract

Let $R_k({\alpha})$, $0{\leq}{\alpha}<1$, $k{\geq}2$ denote certain subclasses of analytic functions in the unit disc E with bounded radius rotation. A function f, analytic in E and given by $f(z)=z+{\sum_{m=2}^{\infty}}a_m{z^m}$, is said to be in the family $R_k(n,{\alpha})n{\in}N_o=\{0,1,2,{\cdots}\}$ and * denotes the Hadamard product. The classes $R_k(n,{\alpha})$ are investigated and same properties are given. It is shown that $R_k(n+1,{\alpha}){\subset}R_k(n,{\alpha})$ for each n. Some integral operators defined on $R_k(n,{\alpha})$ are also studied.

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References

  1. Trans. Amer. Math. Soc. v.135 Convex and starlike univalent functions S. Bernardi
  2. Univalent Functions A.W. Goodman
  3. Proc. Amer. Math. Soc. v.16 Some classes of regular univalent functions R.J. Libera
  4. Proc. Amer. Math. Soc. v.17 On the radius of univalence of certain analytic functions A.E. Livingston
  5. Internat. J. Math. & Math. Sci. v.15 On subclasses of close-to-convex functions of higher order K.I. Noor
  6. Bull. Amer. Math. Soc. v.81 Differential inequalities and Caratheodory functions S. Miller
  7. I.J. Math. v.10 Functions with bounded boundary rotation B. Pinchuk
  8. Comment. Math. Helv. v.48 Hadamard products of schlicht functions and the Polya-Schoenberg conjecture S. Ruscheweyh;T. Shiel-Small
  9. Proc. Amer. Math. Soc. v.77 Integrals of certain univalent functions R. Singh;S. Singh