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New Subclasses of Harmonic Starlike and Convex Functions

  • Porwal, Saurabh (Department of Mathematics, U. I. E. T. Campus, C. S. J. M. University) ;
  • Dixit, Kaushal Kishore (Department of Engineering Mathematics, Gwalior Institute of Information Technology)
  • Received : 2011.10.04
  • Accepted : 2012.11.07
  • Published : 2013.09.23

Abstract

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

Keywords

References

  1. O. P. Ahuja, Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math., 6(4)(2005), Art. 122, 1-18.
  2. Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect., A44(1990), 1-7.
  3. 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
  4. K. K. Dixit and Vikas Chandra, On subclass of univalent functions with positive coefficients, Aligarh Bull. Math., 27(2)(2008), 87-93.
  5. K. K. Dixit and A. L. Pathak, A new class of analytic functions with positive coefficients, Indian J. Pure Appl. Math., 34(2)(2003), 209-218.
  6. K. K. Dixit and Saurabh Porwal, A subclass of harmonic univalent functions with positive coefficients, Tamkang J. Math., 41(3)(2010), 261-269.
  7. P. Duren, Harmonic mappings in the plane, Camb. Univ. Press, (2004).
  8. 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
  9. S. Ponnusamy and A. Rasila, Planar harmonic mappings, Ramanujan Mathematical Society Mathematics Newsletters, 17(2)(2007), 40-57.
  10. S. Ponnusamy and A. Rasila, Planar harmonic and quasi-conformal mappings, Ramanujan Mathematical Society Mathematics Newsletters, 17(3)(2007), 85-101.
  11. Saurabh Porwal and K. K. Dixit, An application of certain convolution operator involving hypergeometric functions, J. Raj. Acad. Phy. Sci., 9(2)(2010), 173-186.
  12. Saurabh Porwal, K. K. Dixit, Vinod Kumar and Poonam Dixit, On a subclass of analytic functions defined by convolution, General Mathematics, General Mathematics, 19(3)(2011), 57-65.
  13. 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
  14. H. Silverman, Harmonic univalent function with negative coefficients, J. Math. Anal. Appl., 220(1998), 283-289. https://doi.org/10.1006/jmaa.1997.5882
  15. H. Silverman, E. M. Silvia, Subclasses of Harmonic univalent functions, New Zealand. J. Math., 28(1999), 275-284.
  16. B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Univalent functions with positive coefficients, Tamkang J. Math., 25(1994), 225-230.
  17. B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Close-to-Convex functions with positive coefficients, Studia Univ. Babes-Balyai, Mathematica, XL4(1995), 25-31.

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