Second Hankel Determinant for Analytic Functions Defined by Ruscheweyh Derivative

Article Sidebar

PDF
Cite as:
T. Yavuz, Second Hankel Determinant for Analytic Functions Defined by Ruscheweyh Derivative, Int. J. Anal. Appl., 8 (1) (2015), 63-68.

Main Article Content

T. Yavuz

Abstract

Let S denote the class of analytic and univalent functions in the open unit disk D= {z:|z|<1} with the normalization conditions. In the present article an upper bound for the second Hankel determinant |aâ‚‚aâ‚„-a₃ ²| is obtained for the analytic functions defined by Ruscheweyh derivative.

Article Details

References

  1. P. L. Duren, Univalent Functions, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
  2. R. Ehrenborg, The Hankel determinant of exponantial polynomials. American Mathematical Monthly, 107 (2000), 557-560.
  3. M. Fekete and G. Szeg ¨o, Eine Bemerkung uber ungerade schlichte Funktionen, J. London Math. Soc, 8 (1933), 85-89.
  4. U. Grenander and G. Szeg ¨o, Toeplitz forms and their application, Univ. of Calofornia Press, Berkely and Los Angeles, (1958).
  5. T. Hayami and S. Owa, Hankel determinant for p-valently starlike and convex functions of order α, General Math., 17 (2009), 29-44.
  6. T. Hayami and S. Owa, Generalized Hankel determinant for certain classes, Int. J. Math. Anal., 4 (2010), 2573-2585.
  7. A. Janteng, S. A. Halim, and M. Darus, Coefficient inequality for a function whose derivative has positive real part, J. Ineq. Pure and Appl. Math, 7 (2) (2006), 1-5.
  8. A. Janteng, Halim, S. A. and Darus, M. : Hankel Determinant For Starlike and Convex Functions, Int. Journal of Math. Analysis, I (13) (2007), 619-625.
  9. J. W. Layman, The Hankel transform and some of its properties. J. of integer sequences, 4 (2001), 1-11.
  10. R.J. Libera, and E.J. Zlotkiewicz, Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc., 85(2) (1982), 225-230.
  11. R.J. Libera, and E.J. Zlotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc., 87(2) (1983), 251-289.
  12. G. Murugusundaramoorthy and N. Magesh, Coefficient Inequalities For Certain Classes of Analytic Functions Associated with Hankel Determinant, Bulletin of Math. Anal. Appl., I (3) (2009), 85-89.
  13. J. W. Noonan and D. K. Thomas, On the second Hankel Determinant of a really mean p valent functions, Trans. Amer. Math. Soc, 223 (2) (1976), 337-346.
  14. K. I. Noor, Hankel determinant problem for the class of functions with bounded boundary rotation. Rev. Roum. Math. Pures Et Appl, 28 (8) (1983), 731-739.
  15. S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975) 109- 115.
  16. R. Singh, S. Singh, Integrals of certain univalent functions, Proc. Amer. Math. Soc. 77 (1979) 336-340.
  17. S. C. Soh and D. Mohamad, Coefficient Bounds For Certain Classes of Close-to-Convex Functions, Int. Journal of Math. Analysis, 2 (27) (2008), 1343-1351.
  18. T. Yavuz, Second hankel determinant problem for a certain subclass of univalent functions, International Journal of Mathematical Analysis Vol. 9(10), (2015), 493 - 498.