Upper Bound of the Third Hankel Determinant for a Subclass of Analytic Functions Subordinate to Cosine Function

Authors

  • Khurshid Ahmad Government Post Graduate Collage Dargai, Malakand, Pakistan
  • Serkan Araci Department of Economics, Faculty of Economics Administrative and Social Sciences Hasan Kalyoncu University TR-27410 Gaziantep, Turkey
  • Mirajul Haq Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
  • Bilal Khan School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, EasChina Normal University, 500 Dongchuan Road, Shanghai 200241, Peoples Republic of China

DOI:

https://doi.org/10.21015/vtm.v8i1.392

Abstract

In this paper, we define a new subclass of analytic functions involving the cosine functions. For this function class, we obtain the upper bound of the third Hankel determinant.

References

Abdullah A., Arif, M., Alghamdi, M. A., and Hussain, S., Starlikness associated

with cosine hyperbolic function, Mathematics, 8, 1118, (2020).

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

analytic functions, J. Ineq. Appl., (1); Art. 22, 7 pages, (2012).

Arif, M., Raza, M., Tang, H., Hussain, S., 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.; Rani, L.; Raza, M.; Zaprawa, P. Fourth Hankel determinant for the

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

(2018).

Babalola, K. O. On H

(1) Hankel determinant for some classes of univalent

functions, Ineq. Theory Appl. 6, 1-7, (2007).

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,

(2021).

Cho, N. E.; Kumar, S.; Kumar, V.; Ravichandran, V.; Srivastava, H.M.

Starlike functions related to the Bell numbers. Symmetry, 11, 219,

doi.10.33901sym11020219, (2019).

Duren, P. L.Univalent junctions, Springer Verlag. New York Inc. (1983).

Dzoik, J.; Raina, R. K.; Sokó÷, J. On certain subclasses of starlike functions

related to a shell-like curve connected with Fibonacci numbers. Math. Comput.

Model. 57, 1203-1211, (2013).

Goel, P.; Kumar, S. Certain class of starlike functions associated with Modi ed

sigmoid function. Bull. Malays. Math. Sci. Soc. 43, 957991, (2019).

Hu, Q., Srivastava, H. M., Ahmad, B., Khan, N., Khan, M. G., Mashwani, W.

K., and Khan, B. A subclass of multivalent Janowski type q-Starlike functions

and its consequences, Symmetry 13, 1275, (2021).

Islam, S., Khan, M. G., Ahmad, B., Arif, M., Chinram, R., Q-extension of starlike

functions subordinated with a trigonometric sine function, Mathematics, 8,

; doi:10.3390/math8101676, (2020).

Janteng, A. Abdulhalirn, S and Darus, M. Coe¢ cient inequality for a function

whose derivative has positive real part, J. Ineq. Pure Appl. Math. 50, 1-5,

(2006).

Janowski, W. Extremal problems for a family of functions with positive real

part and for some related families. Ann. Pol. Math. 23, 159177, (1970).

Jangteng, A.; Halim, S.A.; Darus, M. Coe¢ cient inequality for a function whose

derivative has a positive real part, J. Ineq. Pure Appl. Math, 7; 15, (2006).

Jangteng, A.; Halim, S.A.; Darus, M. Coe¢ cient inequality for starlike and

convex functions, Int. J. Ineq. Math. Anal, 1; 619625, (2007).

Kanas, S.; R

aducanu, D. Some class of analytic functions related to conic domains.

Mathematica slovaca. 64, 11831196, (2014).

Kumar, S.; Ravichandran, V. A subclass starlike functions associated with rational

function. Southeast Asian Bull. Math. 40, 199-212, (2016).

Khan, M. G., Ahmad, B., Murugusundaramoorthy, G., Chinram, R., and Mashwani,

W. K. Applications of modi ed Sigmoid functions to a class of starlike

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

Ma,W. C. and Minda, D. A uni ed 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), pp. 157-169. Int. Press,

Cambridge (1994)

Ma, W.; Minda, M. A uni ed treatment of some special classes of univalent

functions.In Proceedings of the Conference on Complex Analysis; Li, Z., Ren,

F., Yang, L., Zhang, S. Eds.; Int. Press: Cambridge, MA, USA, pp.157169

(1992).

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

analytic functions, Journal of Applied Mathematics, Article ID 127615, 7 pages,

(2013).

Raza, M., Srivastava, H. M., Arif, M., Ahmad K., Coe¢ cient estimates for a

certain family of analytic functions involving q-derivative operator. The Ramanujan

Journal, 55, 53-71 (2021).

Shi, L. Ali, I., Arif, M., Cho, N. E., Hussain, S., Khan, H., A study of third Hankel

determinant problem for certain subfamilies of analytic functions involving

cardioid domain, Mathematics, 7(5), 418, 15 pages, (2019).

Shi, L., Srivastava, H. M., Arif, M., Hussain, S., Khan H., An investigation

of the third Hankel determinant problem for certain subfamilies of univalent

functions involving the exponential function, Symmetry, 11(5), 14 pages (2019).

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, (2020).

Singh,G. and Singh, G. On the second Hankel determinant for a new subclass

of analytic functions, J. Math. Sci. Appl. 2, 1-3, (2014).

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Published

2022-04-16

How to Cite

Ahmad, K., Araci, S., Haq, M., & Khan, B. (2022). Upper Bound of the Third Hankel Determinant for a Subclass of Analytic Functions Subordinate to Cosine Function. VFAST Transactions on Mathematics, 8(1), 35–44. https://doi.org/10.21015/vtm.v8i1.392