Third Hankel determinant for starlike and convex functions with respect to symmetric points

D. Vamshee Krishna, B. Venkateswarlu, T. RamReddy

Abstract


The objective of this paper is to obtain best possible upper bound to the \(H_{3}(1)\)  Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants.

Keywords


Analytic function; starlike and convex functions with respect to symmetric points; upper bound; Hankel determinant; convolution; positive real function; Toeplitz determinants

Full Text:

PDF

References


Ali, R. M., Coefficients of the inverse of strongly starlike functions, Bull. Malays. Math. Sci. Soc. (second series) 26 (1) (2003), 63-71.

Babalola, K. O., On (H3(1)) Hankel determinant for some classes of univalent functions, Inequality Theory and Applications 6 (2010), 1-7.

Das, R. N., Singh, P., On subclass of schlicht mappings, Indian J. Pure and Appl. Math. 8 (1977), 864-872.

Duren, P. L., Univalent Functions, Springer, New York, 1983.

Grenander, U., Szego, G., Toeplitz Forms and Their Applications, 2nd ed., Chelsea Publishing Co., New York, 1984.

Janteng, A., Halim, S. A., Darus, M., Hankel determinant for starlike and convex functions, Int. J. Math. Anal. (Ruse) 1 (13) (2007), 619-625.

Libera, R. J., Złotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (1983), 251-257.

Pommerenke, Ch., Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.

Pommerenke, Ch., On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc. 41 (1966), 111-122.

Prithvipal Singh , A study of some subclasses of analytic functions in the unit disc, Ph.D. Thesis (1979), I.I.T. Kanpur.

Raja, M., Malik, S. N., Upper bound of third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, J. Inq. Appl. (2013), vol. 2013.

RamReddy, T., A study of certain subclasses of univalent analytic functions, Ph.D. Thesis (1983), I.I.T. Kanpur.

RamReddy, T., Vamshee Krishna, D., Hankel determinant for starlike and convex functions with respect to symmetric points, J. Ind. Math. Soc. (N. S.) 79 (1-4) (2012), 161-171.

Ratanchand, Some aspects of functions analytic in the unit disc, Ph.D. Thesis (1978), I.I.T. Kanpur.

Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75.

Simon, B., Orthogonal Polynomials on the Unit Circle, Part 1. Classical Theory, American Mathematical Society, Providence (RI), 2005.

Vamshee Krishna, D., Venkateswarlu, B., RamReddy, T., Third Hankel determinant for certain subclass of p-valent functions, Complex Var. and Elliptic Eqns. 60 (9) (2015), 1301-1307.

Vamshee Krishna, D., RamReddy, T., Coefficient inequality for certain p-valent analytic functions, Rocky Mountain J. Math. 44 (6) (2014), 941-1959.




DOI: http://dx.doi.org/10.17951/a.2016.70.1.37
Date of publication: 2016-07-04 15:44:00
Date of submission: 2016-07-04 12:10:16


Statistics


Total abstract view - 1381
Downloads (from 2020-06-17) - PDF - 801

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 D. Vamshee Krishna, B. Venkateswarlu, T. RamReddy