A Study of Fourth Hankel Determinant of Certain Analytic Function

Neelam Khan, Nazar Khan, Basem Aref Frasin, Mirajul Haq, Bilal Khan


The main motive of this paper is to nd an upper bound of the fourth Hankel determinant H 4;1 (f) for a subclass S; with hyperbolic domain.

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Ahuja, O. P., and Jahangiri, M. Fekete-Szego problem for a unied class of

analytic functions. Panamerican Mathematical Journal, 7, 67-78, (1997).

Arif, M. Noor, K. I. Raza, M. Hankel determinant problem of a subclass of

analytic functions, J. Inequality Applications, (2012), doi:10.1186/1029-242X2012-22.

Arif, M., Rani, L., Raza, M., and Zaprawa, P. Fourth Hankel determinant for

the set of star-like functions. Mathematical Problems in Engineering, 2021.

Arif, M., Rani, L., Raza, M., and Zaprawa, P. Fourth Hankel determinant for

the family of functions with bounded turning. Bulletin of the Korean Mathematical

Society, 55(6), 1703-1711, (2018).

Arif, M., Raza, M., Tang, H., Hussain, S., and Khan, H. Hankel determinant of

order three for familiar subsets of analytic functions related with sine function.

Open Mathematics, 17(1), 1615-1630, (2019).

Arif, M. Noor, K. I. Raza, M, Haq, W. Some properties of a generalized class

of analytic functions related with Janowski functions, Abstract and Applied

Analysis, article ID 279843 (2012).

Arif, M.; Rani, L.; Raza, M.; Zaprawa, P. Fourth Hankel determinant for the

family of functions with bounded turning. Bull. Kor. Math. Soc, 55, 17031711


Babalola, K. O. On H

(3) Hankel determinant for some classes of univalent

functions. arXiv preprint arXiv:0910.3779 (2009).

Barukab, O., Arif, M., Abbas, M., Khan, S. K., Sharp bounds of the coe¢ cient

results for the family of bounded turning functions associated with petal shaped

domain, Journal of Function Spaces, Volume 2021, Article ID 5535629, 9 pages,

Fekete M. and Szegö G., Eine bemerkung uber ungerade schlichte funktionen,

J. London Math. Soc. (8) 85-89, doi: 10.1112/s1-8.2.85, (1993).

Hussain S., Arif M. and Malik S. N., Higher order close-to-convex functions

associated with Attiya-Sriwastawa operator, Bull. Iranian Math. Soc. 40(4),

-920, (2014).

Janteng, A. Halim, S. A, Darus, M. Hankel determinant for starlike and convex

functions, Int. J. Math. Anal. 1(13), 619-625, (2007).

Kanas S., Coe¢ cient estimates in subclasses of the Catheodory class related to

conical domains, Acta Math. Univ. Comenian. 74(2), 149-161, (2005).

Khan, G. K.; Ahmad. B.; Murugusundaramoorthy, G..; Chinram, R.; Mashwani,

W. K.; . Applications of modied Sigmoid functions to a class of starlike

functions. J. Funct. Spaces, 8, Article ID: 8844814, (2020).

Layman, J. W. The Hankel transform and some of its properties, J. Integer

seq., 4(1), 1-11, (2001).

Libra, R.J, Zlotkiewicz, E.J. Early coe¢ cient of the inverse of a regular convex

function, Proc. Am. Math. Soc. 85(2), 225-230, (1982).

Ma, W. C. Minda, D. A unied treatment of some special classes of univalent

functions, In. Li, Z, Ren, F, Yang, L, Zhang, S (eds.) Proceeding of the conference

on Complex Analysis (Tianjin, 1992), 157-169. Int. Press, Cambridge


Ma, WC, Minda, D: A unied treatment of some special classes of univalent

functions. In: Li, Z, Ren, F, Yang, L, Zhang, S(eds). Proceedings of the conference

on Complex Analysis(Tianjin, 1992) Int. Press Cambridge. 157-169,


Noor K. I. and Malik S.N., On coe¢ cient inequalities of functions associated

with conic domains, Comput. Math. Appl. 62, 2209-2217, (2011)

Noonan, J. W, Thomas, D. K. On second Hankel determinant of a really mean

p-valent functions, Trans. Amer. Math. Soc., 223(2), 337-346, (1976).

Raza, M. Malik, S. N. Upper bound of the third Hankel determinant for a class

of analytic functions related with with the lemniscate of Bernoulli, Journal of

Inequality and Applications, (2013) doi:10.1186/1029-242X-2013-412.

Ravichandran, V., Verma, S.: Bound for the fth coe¢ cient of certain starlike

functions. C.R. Math. 353(6). 505-510, (2015).

Raza, M., Arif, M., Darus, M., Fekete-Szego inequality for a subclass of p-valent

analytic functions, Journal of Applied Mathematics, Volume, Article ID 127615,

pages, (2013).

Shi, L., Wang, Z-G., Su, R-L., Arif, M., Initial successive coe¢ cients for certain

classes of univalent functions involving the exponential function, Journal of

Mathematical Inequalities, Volume 14, 4, 1183 1201, (2021).

Tang, H.; Arif, M.; Haq, M.; Khan, N.; Khan, M.; Ahmad, K.; Khan, B. Fourth

Hankel Determinant Problem Based on Certain Analytic Functions. Symmetry,

, 663, (2022). https://doi.org/10.3390/sym14040663.

Zhang C, Haq M, Khan N, Arif M, Ahmad K, Khan B. Radius of StarLikeness

for Certain Subclasses of Analytic Functions. Symmetry (20738994).

Dec 1;13(12), (2021).

DOI: http://dx.doi.org/10.21015/vtm.v9i1.1019


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