Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NEIGHBORHOODS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Darwish, Hanan E. (Department of Mathematics Faculty of Science Mansoura University) ;
  • Aouf, Mohamed K. (Department of Mathematics Faculty of Science Mansoura University)
  • Received : 2009.07.20
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

The main object of this paper is to prove several inclusion relations associated with (j, ${\delta}$)-neighborhoods of various subclasses defined by Salagean operator by making use of the familiar concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.

Keywords

References

  1. O. Altintas and S. Owa, Neighborhoods of certain analytic functions with negative coefficients, Internat. J. Math. Math. Sci. 19 (1996), no. 4, 797-800. https://doi.org/10.1155/S016117129600110X
  2. O. Altintas, O. Ozkan, and H. M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Lett. 13 (2000), no. 3, 63-67. https://doi.org/10.1016/S0893-9659(99)00187-1
  3. M. K. Aouf, Neighborhoods of certain classes of analytic functions with negative coefficients, Int. J. Math. Math. Sci. 2006 (2006), Art. ID 38258, 6 pp.
  4. M. K. Aouf, H. E. Darwish, and A. A. Attiya, Generalization of certain subclasses of analytic functions with negative coefficients, Studia Univ. Babes-Bolyai Math. 45 (2000), no. 1, 11-22.
  5. M. K. Aouf, H. M. Hossen, and A. Y. Lashin, On certain families of analytic functions with negative coefficients, Indian J. Pure Appl. Math. 31 (2000), no. 8, 999-1015.
  6. S. K. Chatterjea, On starlike functions, J. Pure Math. 1 (1981), 23-26.
  7. A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601. https://doi.org/10.1090/S0002-9939-1957-0086879-9
  8. H. M. Hossen, G. S. Salagean, and M. K. Aouf, Notes on certain classes of analytic functions with negative coefficients, Mathematica 39(62) (1997), no. 2, 165-179.
  9. H. Orhan and M. Kamali, Neighborhoods of a class of analytic functions with negative coefficients, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 21 (2005), no. 1, 55-61.
  10. St. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521-527. https://doi.org/10.1090/S0002-9939-1981-0601721-6
  11. G. S. Salagean, Subclasses of univalent functions, Complex analysis-fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983.
  12. T. Sekine, Generalization of certain subclasses of analytic functions, Internat. J. Math. Math. Sci. 10 (1987), no. 4, 725-732. https://doi.org/10.1155/S0161171287000826
  13. H. M. Srivastava, S. Owa, and S. K. Chatterjea, A note on certain classes of starlike functions, Rend. Sem. Mat. Univ. Padova 77 (1987), 115-124.