Coefficient Inequalities for Certain Subclasses of Analytic Functions Defined by Using a General Derivative Operator

  • Bulut, Serap (Kocaeli University, Civil Aviation College, Arslanbey Campus)
  • Received : 2009.12.02
  • Accepted : 2011.09.14
  • Published : 2011.09.23


In this paper, we define new classes of analytic functions using a general derivative operator which is a unification of the S$\breve{a}$l$\breve{a}$gean derivative operator, the Owa-Srivastava fractional calculus operator and the Al-Oboudi operator, and discuss some coefficient inequalities for functions belong to this classes.


  1. M. Acu and S. Owa, Convex functions associated with some hyperbola, J. Approx. Theory Appl., 1(2005), 37-40.
  2. F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 2004, no. 25-28, 1429-1436.
  3. F. M. Al-Oboudi and K. A. Al-Amoudi, On classes of analytic functions related to conic domains, J. Math. Anal. Appl., 339(2008), 655-667.
  4. R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 28(1997), 17-32.
  5. C. Caratheodory, Uber den variabilit¨atsbereich der Fourier'schen konstanten von possitiven harmonischen funktionen, Rend. Circ. Palermo, 32(1911), 193-217.
  6. B. A. Frasin, Family of analytic functions of complex order, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 22(2006), 179-191.
  7. A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1991), 87-92.
  8. S. Owa, On the distortion theorems. I, Kyungpook Math. J. 18(1978), 53-59.
  9. S. Owa, Y. Polatoglu and E. Yavuz, Coefficient inequalities for classes of uniformly starlike and convex functions, J. Inequal. Pure Appl. Math., 7(2006), Article 160, 5 pp.
  10. S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077.
  11. M. S. Robertson, On the theory of univalent functions, Ann. of Math., 37(2)(1936), 374-408.
  12. F. Ronning, On starlike functions associated with parabolic regions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 45(1991), 117-122.
  13. F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. ,118(1993), 189-196.
  14. 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.
  15. S. Shams, S. R. Kulkarni and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci., 55(2004), 2959-2961.
  16. H. M. Srivastava, A. K. Mishra and M. K. Das, A nested class of analytic functions defined by fractional calculus, Commun. Appl. Anal., 2(1998), 321-332.
  17. H. M. Srivastava and A. K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Comput. Math. Appl., 39(2000), 57-69.
  18. H. M. Srivastava and S. Owa, (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, Ellis Horwood Series: Mathematics and Its Applications, Ellis Horwood, Chichester, UK; JohnWiley & Sons, New York, NY, USA, 1989.

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