Keywords:-
Article Content:-
Abstract
The objective of this paper is to obtain a sharp upper bound to the second Hankel determinant H2(2) for the function f(z) when it belongs to the class Sm (; l; ) of Bazilevic functions associated with extended multiplier transformation operator
References:-
References
Abubaker, A., Darus, M., Hankel Determinant for a class of analytic functions involving a
generalized linear dierential operator, Int. J. Pure Appl. Math., 69(2011), no. 4, 429-435.
Sahsene Altinkaya ,Sibel Yalcin, Third hankel determinant for Bazilvic functions., Adavance
in Mathematics Scientic Journal., 5(2016), no. 2, 91-96.
A Catas, On certain classes of p-valent functions dened by Multiplier transformations,In
proceedings of international symposium on Geometric function theory and Applications GFTA
Proceedings , (Istanbul,Turkey,20-24,August2007),91(2008),241-250.
Duren, P.L., Univalent functions, vol. 259 of Grundlehren der Mathematischen Wissenschaften,
Springer, New York, USA, 1983.
Ehrenborg, R., The Hankel determinant of exponential polynomials, Amer. Math. Monthly,
(2000), no. 6, 557-560.
Grenander, U., Szegö, G., Toeplitz forms and their applications, Second edition, 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(2007), no. 13, 619-625.
Janteng, A., Halim, S.A., Darus, M., Coecient inequality for a function whose derivative has
a positive real part, J. Inequal. Pure Appl. Math., 7(2006), no. 2, 1-5.
Krishna, V.D., RamReddy, T., Coecient inequality for certain p-valent analytic functions,
Rocky MT. J. Math., 44(6)(2014), 1941-1959.
Libera, R.J., Zlotkiewicz, E.J., Coecient bounds for the inverse of a function with derivative
in P, Proc. Amer. Math. Soc., 87(1983), no. 2, 251-257.
Mac Gregor, T.H., Functions whose derivative have a positive real part, Trans. Amer. Math.
Soc., 104(1962), no. 3, 532-537.
Mishra, A.K., Gochhayat, P., Second Hankel determinant for a class of analytic functions
dened by fractional derivative, Int. J. Math. Math. Sci., Article ID 153280, 2008, 1-10.
Noonan, J.W., Thomas, D.K., On the second Hankel determinant of areally mean p-valent
functions, Trans. Amer. Math. Soc., 223(1976), no. 2, 337-346.
Pommerenke, Ch., Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975.
Pommerenke, Ch., On the coecients and Hankel determinants of univalent functions, J.
Lond. Math. Soc., 41(1966), 111-122.
Singh, R., On Bazilevic functions, Proc. Amer. Math. Soc., 38(1973), no. 2, 261-271.
Layman J.W, The Hankel transform and some of its properties,J.Intiger seq 4(1)2001,1-11 .
K. I. Noor, Hankel determinant problem for the class of functions with bounded boundary
rotation, Rev. Roum. Math. Pures Et Appl., 28(8) (1983), 731-739.S. M. Patil,
Department of Applied Sciences,
S. S. V. P. S B. S Deore College of Engineering,
Deopur, Dhule, INDIA.
sunitashelar1973@gmail.com
S. M. KHAIRNAR,
Professor & Head,
Department of Applied Sciences,
MIT Academy of Engineering,
Alandi, Pune-412105, INDIA.
smkhairnar2007@gmail.com.