Kyungpook Mathematical Journal

  • 제49권4호
  • /
  • Pages.751-761
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  • 2009
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Properties of Harmonic Functions Defined by Convolution

  • 투고 : 2009.02.01
  • 심사 : 2009.06.03
  • 발행 : 2009.12.31
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초록

In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results.

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참고문헌

  1. Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect.A, 44(1990), 1-7.
  2. J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser.AI Math., 9(1984), 3-25. https://doi.org/10.5186/aasfm.1984.0905
  3. B. A. Frasin, Comprehensive family of harmonic univalent functions, SUT Journal of Mathematics, 42(1)(2006), 145-155.
  4. J. M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl., 235(1999), 470-477. https://doi.org/10.1006/jmaa.1999.6377
  5. M. Ozturk, S. Yalcin and M. Yamankaradeniz, Convex subclass of harmonic starlike functions, Appl. Math. Comput., 154(2004), 449-459. https://doi.org/10.1016/S0096-3003(03)00725-2
  6. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116. https://doi.org/10.1090/S0002-9939-1975-0369678-0
  7. H. Silverman, Harmonic univalent function with negative coefficients, J. Math. Anal. Appl., 220(1998), 283-289. https://doi.org/10.1006/jmaa.1997.5882
  8. H. Silverman, E. M. Silvia, Subclasses of Harmonic univalent functions, New Zealand. J. Math., 28(1999), 275-284.

피인용 문헌

  1. Partial sums of certain harmonic univalent functions vol.32, pp.4, 2011, https://doi.org/10.1134/S1995080211040184
  2. Some properties of a subclass of harmonic univalent functions defined by the multiplier transformations vol.46, pp.3, 2015, https://doi.org/10.1007/s13226-015-0132-9
  3. A Convolution Approach on Partial Sums of Certain Harmonic Univalent Functions vol.2012, 2012, https://doi.org/10.1155/2012/509349