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Neighborhood Properties for Certain Subclasses of Analytic Functions of Complex Order with Negative Coefficients

  • Bulut, Serap (Kocaeli University, Civil Aviation College, Arslanbey Campus)
  • Received : 2012.03.14
  • Accepted : 2013.05.09
  • Published : 2014.06.23

Abstract

In the present investigation, by making use of the familiar concept of neighborhoods of analytic and multivalent functions, we prove several inclusion relations associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of analytic functions of complex order, which are introduced here by means of the Al-Oboudi derivative. Several special cases of the main results are mentioned.

Keywords

References

  1. O. P. Ahuja and M. Nunokawa, Neighborhoods of analytic functions defined by Ruscheweyh derivatives, Math. Japon., 51(2003), 487-492.
  2. F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci., 2004(25-28), 1429-1436.
  3. O. Altintas, Neighborhoods of certain p-valently analytic functions with negative co-efficients, Appl. Math. Comput., 187(2007), 47-53. https://doi.org/10.1016/j.amc.2006.08.101
  4. O. Altntas and S. Owa, Neighborhoods of certain analytic functions with negative coefficients, Int. J. Math. Math. Sci., 19(1996), 797-800. https://doi.org/10.1155/S016117129600110X
  5. O. Altntas, O. Ozkan and H. M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Letters, 13(3)(2000), 63-67.
  6. O. Altntas, O. Ozkan and H. M. Srivastava, Majorization by starlike functions of complex order, Complex Variables Theory Appl., 46(2001), 207-218. https://doi.org/10.1080/17476930108815409
  7. O. Altntas, O. Ozkan and H. M. Srivastava, Neighborhoods of a certain family of mul-tivalent functions with negative coefficients, Comput. Math. Appl., 47(2004), 1667-1672. https://doi.org/10.1016/j.camwa.2004.06.014
  8. S. Bulut, On a class of analytic and multivalent functions with negative co-efficients defined by Al-Oboudi differential operator, Stud. Univ. Babes-Bolyai Math., 55(4)(2010), 115-130.
  9. R. M. El-Ashwah and M. K. Aouf, Inclusion and neighborhood properties of some analytic p-valent functions, Gen. Math., 18(2)(2010), 173-184.
  10. 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
  11. B. S. Keerthi, A. Gangadharan and H. M. Srivastava, Neighborhoods of certain sub-classes of analytic functions of complex order with negative coefficients, Math. Com-put. Modelling, 47(3-4)(2008) 271-277. https://doi.org/10.1016/j.mcm.2007.04.004
  12. G. Murugusundaramoorthy and H. M. Srivastava, Neighborhoods of certain classes of analytic functions of complex order, J. Inequal. Pure Appl. Math., 5(2)(2004), 1-8(Art. 24).
  13. M. A. Nasr and M. K. Aouf, Starlike function of complex order, J. Natur. Sci. Math., 25(1985), 1-12.
  14. H. Orhan, M. Kamali, Starlike, convex and close-to convex functions of complex order, Appl. Math., Comput. 135(2003) 251-262. https://doi.org/10.1016/S0096-3003(01)00326-5
  15. R. K. Raina and H. M. Srivastava, Inclusion and neighborhood properties of some analytic and multivalent functions, J. Inequal. Pure Appl. Math., 7(1)(2006), 1-6(Art. 5).
  16. S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81(1981), 521-527. https://doi.org/10.1090/S0002-9939-1981-0601721-6
  17. G. S. Salagean, Subclasses of univalent functions, Complex Analysis-Fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., vol 1013, Springer Berlin 1983, pp 362-372.
  18. T. N. Shanmugam and M. P. Jeyaraman, Neighborhoods of a class of analytic func-tions with negative coefficients, J. Orissa Math. Soc., 25(1-2)(2006), 83-89.
  19. H. Silverman, Neighborhoods of classes of analytic functions, Far East J. Math. Sci., 3(1995), 165-169.
  20. P. Wiatrowski, On the coefficients of some family of holomorphic functions, Zeszyty Nauk. Uniw. Lodzkiego, Mat.-Przyr., 39(2)(1970), 75-85.