Second Hankel Determinant for Analytic Functions Defined By Linear Operator

Sunita M. Patil; S. M. Khairnar

doi:https://doi.org/10.14445/22315373/IJMTT-V41P525

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 41 | Number 3 | Year 2017 | Article Id. IJMTT-V41P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V41P525

Second Hankel Determinant for Analytic Functions Defined By Linear Operator

Sunita M. Patil, S. M. Khairnar

Abstract

Let S( , n, m) denote the class of analytic and univalent functions in the open unit disk, D = with normalized conditions. In the present article an upper bound for the Second Hankel determinant is obtained for the analytic functions defined by linear operator.

Keywords

Univalent function, Starlike function, convex function, Hankel derminant, Linear Operator.

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. Szego, Eine Bemerkung uber ungerade schlichte Funktionen, J. London Math. Soc, 8 (1933), 85-89.
[4]. U. Grenander and G. Szego, 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 , 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, Coeficient 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 coeficients 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, Coeficient 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, Coeficient 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]. S. Goyal, R. K. Laddha, On the generalized Riemann zeta function and the generalized Lambert transform, Ganita Sandesh, 11(1997), 99-108.
[17]. C. Soh and D. Mohamad, Coeficient 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.

Citation :

Sunita M. Patil, S. M. Khairnar, "Second Hankel Determinant for Analytic Functions Defined By Linear Operator," International Journal of Mathematics Trends and Technology (IJMTT), vol. 41, no. 3, pp. 272-274, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V41P525