Third Hankel determinant for starlike and convex functions with respect to symmetric points
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 70 (2016) no. 1

Voir la notice de l'article provenant de la source Library of Science

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
@article{AUM_2016_70_1_a6,
     author = {Vamshee Krishna, D. and Venkateswarlu, B. and RamReddy, T.},
     title = {Third {Hankel} determinant for starlike and convex functions with respect to symmetric points},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica},
     publisher = {mathdoc},
     volume = {70},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a6/}
}
TY  - JOUR
AU  - Vamshee Krishna, D.
AU  - Venkateswarlu, B.
AU  - RamReddy, T.
TI  - Third Hankel determinant for starlike and convex functions with respect to symmetric points
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica
PY  - 2016
VL  - 70
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a6/
LA  - en
ID  - AUM_2016_70_1_a6
ER  - 
%0 Journal Article
%A Vamshee Krishna, D.
%A Venkateswarlu, B.
%A RamReddy, T.
%T Third Hankel determinant for starlike and convex functions with respect to symmetric points
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica
%D 2016
%V 70
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a6/
%G en
%F AUM_2016_70_1_a6
Vamshee Krishna, D.; Venkateswarlu, B.; RamReddy, T. Third Hankel determinant for starlike and convex functions with respect to symmetric points. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 70 (2016) no. 1. http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a6/

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

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

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

[4] Duren, P. L., Univalent Functions, Springer, New York, 1983.

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

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

[7] 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.

[8] Pommerenke, Ch., Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.

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

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

[11] 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.

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

[13] 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.

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

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

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

[17] 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.

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