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NOTES ON CERTAIN HARMONIC STARLIKE MAPPINGS

Year 2014, Volume: 4 Issue: 1, 20 - 26, 01.06.2014

Abstract

Complex-valued harmonic functions that are univalent and sense-preserving in the unit disk D can be written in the form f = h + ¯g, where h and g are analytic in D. We give some inequalities for normalized harmonic functions that are starlike.

References

  • Clunie, J., and Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. MR 752388 (85i:30014)
  • Duren, P., Harmonic Mappings in the Plane, Cambridge Tracts in Mathematics, vol. 156, Cambridge University Press, Cambridge, 2004. MR 2048384 (2005d:31001)
  • Goodman, A.W., Univalent Functions. Vol. I and Vol. II, Mariner Publishing Co. Inc., Tampa, FL, 1983. MR 704183 (85j:30035a)
  • Sheil-Small, T., Constants for planar harmonic mappings, J. London Math. Soc. (2) 42 (1990), 237- 248. MR 1083443 (91k:30052)
Year 2014, Volume: 4 Issue: 1, 20 - 26, 01.06.2014

Abstract

References

  • Clunie, J., and Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. MR 752388 (85i:30014)
  • Duren, P., Harmonic Mappings in the Plane, Cambridge Tracts in Mathematics, vol. 156, Cambridge University Press, Cambridge, 2004. MR 2048384 (2005d:31001)
  • Goodman, A.W., Univalent Functions. Vol. I and Vol. II, Mariner Publishing Co. Inc., Tampa, FL, 1983. MR 704183 (85j:30035a)
  • Sheil-Small, T., Constants for planar harmonic mappings, J. London Math. Soc. (2) 42 (1990), 237- 248. MR 1083443 (91k:30052)
There are 4 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. Yavuz Duman This is me

S. Owa This is me

Publication Date June 1, 2014
Published in Issue Year 2014 Volume: 4 Issue: 1

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