Bound on H3(1) Hankel determinant for pre-starlike functions of order α.

• Krishna, D. Vamshee ^[1] ; Shalini, D. ^[2]
  1. [1] GITAM University

     GITAM University

     India

     
  2. [2] Sri Venkateswara College of Engineering and Technology.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 2, 2018, págs. 305-315
• Idioma: inglés
• DOI: 10.4067/s0716-09172018000200305
• Enlaces
  • Texto completo
• Resumen

  • The objective of this paper is to obtain best possible upper bound to the third Hankel determinant for the pre-starlike functions of order α (0 ≤ α < 1), using Toeplitz determinants.

• Referencias bibliográficas
  • R. M. Ali, Coefficients of the inverse of strongly starlike functions, Bull. Malays. Math. Sci. Soc., (2nd Series), 26 (1), pp. 63-71, (2003).
  • K. O. Babalola, On H3(1) Hankel determinant for some classes of univalent functions, Inequality Theory and Applications, 6, pp. 1-7, (2010).
  • L. de Branges de Bourcia, A proof of Bieberbach conjecture, Acta Mathematica, 154 (1-2), pp. 137-152, (1985).
  • P. L. Duren, Univalent functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, (1983).
  • U. Grenander and G. Szegö, Toeplitz forms and their applications. 2nd ed. New York (NY): Chelsea Publishing Co., (1984).
  • A. Janteng, S. A. Halim and M. Darus, Hankel Determinant for starlike and convex functions, Int. J. Math. Anal. (Ruse), 1 (13), pp. 619-625,...
  • 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),...
  • Ch. Pommerenke, Univalent functions, Gottingen: Vandenhoeck and Ruprecht; (1975).
  • Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., s1-41 (1), pp. 111-122, (1966).
  • St. Ruscheweyh, Linear operators between classes of pre-starlike functions, Comm. Math. Helv., 52, pp. 497-509, (1977).
  • H. Silverman and E. M. Silvia, Pre-starlike functions with negative coefficients, Int. J. Math. Math. Sci., 2 (3), pp. 427-439, (1979).
  • B. Simon, Orthogonal polynomials on the unit circle, part 1. Classical theory. Vol. 54, American mathematical society colloquium publications....
  • D. Vamshee Krishna and T. RamReddy, Coefficient inequality for parabolic star like functions of order alpha, Afr. Mat., 27 (1-2), pp. 121-132,...
  • D. Vamshee Krishna and T. RamReddy, An upper bound to the second Hankel determinant for pre-star like functions of order α, Le Matematiche,...
  • D. Vamshee Krishna and T. RamReddy, Coefficient inequality for certain p− valent analytic functions, Rocky Mountain J. Math., 44 (6), pp....