Third Hankel determinant for a subclass of analytic univalent functions

T.V. Sudharsan; S.P. Vijayalakshmi; B. Adolf Stephen

doi:10.26637/mjm204/011

Abstract

This paper focuses on attaining the upper bounds on $H_3(1)$ for a class $C_\alpha^\beta(0 \leq \beta<1, \alpha \geq 0)$ in the unit $\operatorname{disk} \Delta=\{z \in \mathbb{C}:|z|<1\}$ .

Keywords:

Analytic functions

Mathematics Subject Classification:

30C45, 30C50

Authors Imprint References Funding Related Articles Downloads

T.V. Sudharsan Department of Mathematics, SIVET College, Chennai - 600 073, Tamil Nadu, India. https://orcid.org/0000-0002-6882-3367
S.P. Vijayalakshmi Department of Mathematics, Ethiraj College, Chennai - 600 008, Tamil Nadu, India.
B. Adolf Stephen Department of Mathematics, Madras Christian College, Chennai - 600 059, Tamil Nadu, India.

Pages: 438-444
Date Published: 01-10-2014
Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

K.O. Babalola, On H 3 (1) Hankel determinant for some classes of univalent functions, Inequality Theory and Applications, S.S. Dragomir and J.Y. Cho, Editors, Nova Science Publishers, 6(2010), 1–7.

K.O. Babalola and T.O. Opoola, On the coefficients of certain analytic and univalent functions, Advances in Inequalities for Series, (Edited by S.S. Dragomir and A. Sofo), Nova Science Publishers, (2006), 5–17.

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

R.M. Goel and B.S. Mehrok, A class of univalent functions, J. Austral. Math. Soc., (Series A), 35(1983), 1-17. DOI: https://doi.org/10.1017/S1446788700024733

T. Hayami and S. Owa, Generalized Hankel determinant for certain classes, Int. Journal of Math. Analysis, $4(52)(2010), 2473-2585$.

A. Janteng, S.A. Halim and M. Darus, Estimate on the second Hankel functional for functions whose derivative has a positive real part, Journal of Quality Measurement and Analysis, 4(1)(2008), 189-195.

N. Kharudin, A. Akbarally, D. Mohamad and S.C. Soh, The second Hankel determinant for the class of close to convex functions, European Journal of Scientific Research, 66(3)(2011), 421-427.

R.J. Libera and E.J. Zlotkiewiez, Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc., 85(2)(1982), 225-230. DOI: https://doi.org/10.1090/S0002-9939-1982-0652447-5

R.J. Libera and E.J. Zlotkiewiez, Coefficient bounds for the inverse of a function with derivative in $P$, Proc. Amer. Math. Soc., 87(2)(1983), 251-257. DOI: https://doi.org/10.1090/S0002-9939-1983-0681830-8

T.H. MacGregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc., 104(1962), $532-537$. DOI: https://doi.org/10.1090/S0002-9947-1962-0140674-7

K.I. Noor, Hankel determinant problem for the class of functions with bounded boundary rotation, Rev. Roum. Math. Pures Et Appl., 28(c)(1983), 731-739.

M.S. Robertson, On the theory of univalent functions, Annals of Math., 37(1936), 374-408. DOI: https://doi.org/10.2307/1968451

C. Selvaraj and N. Vasanthi, Coefficient bounds for certain subclasses of close-to-convex functions, Int. Journal of Math. Analysis, 4(37)(2010), 1807-1814.

G. Shanmugam, B. Adolf Stephen and K.G. Subramanian, Second Hankel determinant for certain classes of analytic functions, Bonfring International Journal of Data Mining, 2(2) (2012), 57–60. DOI: https://doi.org/10.9756/BIJDM.1368