Radius Problem for Subclasses of Harmonic Univalent Functions


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Authors

  • Vadivelan Urkalan Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Tamil Nadu, India
  • Thomas Rosy Department of Mathematics, Madras Christian College, Tambaram, Chennai, Tamil Nadu, India
  • S. Sunil Varma Department of Mathematics, Madras Christian College, Tambaram, Chennai, Tamil Nadu, India

Keywords:

Univalent functions, Harmonic functions, Goodman-Ronning type functions

Abstract

Let $f=h+\bar{g}$ be harmonic functions in the unit disk $D=\left\{z\in \mathbb{C}:\left|z\right| < 1\right\}$ normalized by $f(0)=0=f_{z} (0)-1$. In this paper we find the radius of the Goodman-Ronning type starlikeness and convexity of $D_{f}^{\varepsilon } =zf_{z} -\varepsilon \bar{z}f_{\bar{z}} \,\, (\left|\varepsilon \right|=1)$, when the coefficients of $h$ and $g$ satisfy the harmonic Bieberbach coefficients conjecture conditions.

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Published

15-09-2018

How to Cite

Vadivelan Urkalan, Thomas Rosy, & S. Sunil Varma. (2018). Radius Problem for Subclasses of Harmonic Univalent Functions. International Journal of Mathematics And Its Applications, 6(3), 369–375. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/392

Issue

Vol. 6 No. 3 (2018)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.