Second Hankel Determinant for Analytic Functions Defined By Linear Operator

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-41 Number-3
Year of Publication : 2017
Authors : Sunita M. Patil, S. M. Khairnar
  10.14445/22315373/IJMTT-V41P525

MLA

Sunita M. Patil, S. M. Khairnar "Second Hankel Determinant for Analytic Functions Defined By Linear Operator ", International Journal of Mathematics Trends and Technology (IJMTT). V41(3):272-274 January 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

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.

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.

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