Abstract
In this paper, we obtain sharp upper bound to the second Hankel determinant for the functions belong to the class of λ- pseudo starlike functions, an interesting sub class of univalent functions defined in the open unit disc E={z:|z|<1}, using Toeplitz determinants.
Keywords
Analytic function λ- pseudo-starlike function upper bound second Hankel functional positive real function Toeplitz determinants
References
- Alexander, J. W., Functions which map the interior of the unit circle upon simple regions, Annals. Math., 17(1915), 12 -22.
- Babalola, K. O., On λ-Pseudo- star like functions, J. Classical Anal., 3(2)(2013), 137-147.
- de Branges de Bourcia, Louis, A proof of Bieberbach conjecture, Acta Math., 154(1-2)(1985), 137-152.
- Duren, P. L., Univalent functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 1983.
- Grenander U. and Szegö, G., Toeplitz forms and their applications. 2nd ed., New York (NY): Chelsea Publishing Co., 1984.
- Janteng, A., Halim S. A. and Darus, M., Hankel Determinant for starlike and convex functions, Int. J. Math. Anal., 1(13)(2007), 619-625.
- Libera R. J. and Zlotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in [mathscr]<LaTeX>\mathscr{P}</LaTeX>, Proc. Amer. Math. Soc., 87(2)(1983), 251-257.
- Prajapat, J. K., Bansal, D., Singh Alok and Mishra, A. K., Bounds on third Hankel determinant for close-to-convex functions, Acta. Univ. Sapientiae, Mathematica, 7(2)(2015), 210-219.
- Pommerenke, Ch., Univalent functions, Gottingen: Vandenhoeck and Ruprecht; 1975.
- Pommerenke, Ch., On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., s1-41(1) (1966), 111-122.
- Simon, B., Orthogonal polynomials on the unit circle, part 1. Classical theory. Vol.54, American mathematical society colloquium publications. Providence (RI): American Mathematical Society; 2005.
- Vamshee Krishna D. and RamReddy, T., Coefficient inequality for multivalent bounded turning functions of order alpha, Probl. Anal. Issues Anal., 23(1)(2016), 45-54.
- Vamshee Krishna D. and RamReddy, T., An upper bound to the second Hankel functional for the class of gamma- star like functions, Bull. Iran. Math. Soc., 41(6)(2015), 1327-1337.
- Vamshee Krishna D. and RamReddy, T., Coefficient inequality for a function whose derivative has a positive real part of order alpha, Math. Bohem., 140(1)(2015), 43-52.
- Vamshee Krishna D. and RamReddy, T., Coefficient inequality for certain p-valent analytic functions, Rocky Mountain J. Math., 44(6)(2014), 1941-1959.
Abstract
References
- Alexander, J. W., Functions which map the interior of the unit circle upon simple regions, Annals. Math., 17(1915), 12 -22.
- Babalola, K. O., On λ-Pseudo- star like functions, J. Classical Anal., 3(2)(2013), 137-147.
- de Branges de Bourcia, Louis, A proof of Bieberbach conjecture, Acta Math., 154(1-2)(1985), 137-152.
- Duren, P. L., Univalent functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 1983.
- Grenander U. and Szegö, G., Toeplitz forms and their applications. 2nd ed., New York (NY): Chelsea Publishing Co., 1984.
- Janteng, A., Halim S. A. and Darus, M., Hankel Determinant for starlike and convex functions, Int. J. Math. Anal., 1(13)(2007), 619-625.
- Libera R. J. and Zlotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in [mathscr]<LaTeX>\mathscr{P}</LaTeX>, Proc. Amer. Math. Soc., 87(2)(1983), 251-257.
- Prajapat, J. K., Bansal, D., Singh Alok and Mishra, A. K., Bounds on third Hankel determinant for close-to-convex functions, Acta. Univ. Sapientiae, Mathematica, 7(2)(2015), 210-219.
- Pommerenke, Ch., Univalent functions, Gottingen: Vandenhoeck and Ruprecht; 1975.
- Pommerenke, Ch., On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., s1-41(1) (1966), 111-122.
- Simon, B., Orthogonal polynomials on the unit circle, part 1. Classical theory. Vol.54, American mathematical society colloquium publications. Providence (RI): American Mathematical Society; 2005.
- Vamshee Krishna D. and RamReddy, T., Coefficient inequality for multivalent bounded turning functions of order alpha, Probl. Anal. Issues Anal., 23(1)(2016), 45-54.
- Vamshee Krishna D. and RamReddy, T., An upper bound to the second Hankel functional for the class of gamma- star like functions, Bull. Iran. Math. Soc., 41(6)(2015), 1327-1337.
- Vamshee Krishna D. and RamReddy, T., Coefficient inequality for a function whose derivative has a positive real part of order alpha, Math. Bohem., 140(1)(2015), 43-52.
- Vamshee Krishna D. and RamReddy, T., Coefficient inequality for certain p-valent analytic functions, Rocky Mountain J. Math., 44(6)(2014), 1941-1959.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | August 5, 2017 |
| Acceptance Date | February 1, 2018 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
