Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Partial Sums of Starlike Harmonic Univalent Functions

  • Received : 2010.04.19
  • Accepted : 2010.09.16
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

Keywords

References

  1. O. P. Ahuja, Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math., 6(4)(2005), 1-18.
  2. J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fen. Series AI Math., 9(1984), 3-25. https://doi.org/10.5186/aasfm.1984.0905
  3. K. K. Dixit and Saurabh Porwal, A convolution approach on partial sums of certain analytic and univalent functions, J. Inequal. Pure Appl. Math., 10(4)(2009), 1-17.
  4. P. Duren, Harmonic mappings in the plane, Camb. Univ. Press, 2004.
  5. B. A. Frasin, Partial sums of certain analytic and univalent functions, Acta Math. Acad. Paed. Nyir., 21(2005), 135-145.
  6. B. A. Frasin, Generalization of partial sums of certain analytic and univalent functions, Appl. Math. Lett., 21(7)(2008), 735-741. https://doi.org/10.1016/j.aml.2007.08.002
  7. J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235(1999), 470-477. https://doi.org/10.1006/jmaa.1999.6377
  8. R. K. Raina and Deepak Bansal, Some properties of a new class of analytic functions defined in terms of a Hadamard product, J. Inequl. Pure Appl. Math., 9(1)(2008), 1-20.
  9. T. Rosy, K. G. Subramanian and G. Murugusundaramoorthy, Neighbourhoods and partial sums of starlike based on Ruscheweyh derivatives, J. Inequl. Pure Appl. Math., 4(4)(2003), 1-8.
  10. H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl., 209(1997), 221-227. https://doi.org/10.1006/jmaa.1997.5361
  11. H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., 220(1998), 283-289. https://doi.org/10.1006/jmaa.1997.5882
  12. E. M. Sivlia, On partial Sums of convex functions of order $\alpha$, Houston J. Math., 11(3)(1985), 397-404.

Cited by

  1. A Convolution Approach on Partial Sums of Certain Harmonic Univalent Functions vol.2012, 2012, https://doi.org/10.1155/2012/509349
  2. Partial sums of starlike harmonic multivalent functions vol.26, pp.1-2, 2015, https://doi.org/10.1007/s13370-013-0188-9
  3. Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator vol.2014, 2014, https://doi.org/10.1155/2014/793709
  4. Partial sums of certain harmonic univalent functions vol.32, pp.4, 2011, https://doi.org/10.1134/S1995080211040184