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Some Properties Subclasses of Analytic Functions

Frasin, Basem Aref

  • Received : 2011.10.13
  • Accepted : 2013.03.27
  • Published : 2014.12.23

Abstract

The object of the present paper is to discuss some interesting properties of analytic functions f(z) associated with the subclasses $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$. Also, radius problems of $\frac{1}{\delta}f({\delta}z)$ for f(z) in the class $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$ are considered.

Keywords

Analytic;univalent functions;Cauchy-Schwarz inequality;radius problems

References

  1. G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math. Springer-Verlag, 1013(1983), 362-372. https://doi.org/10.1007/BFb0066543
  2. Neslihan Uyanik and Shigeyoshi Owa, New extensions for classes of analytic functions associated with close-to-convex and starlike of order ${\alpha}$, Mathematical and Computer Modelling, 54(2011), 359-366. https://doi.org/10.1016/j.mcm.2011.02.020