Bounds of third and fourth Hankel determinants for a generalized subclass of bounded turning functions subordinated to sine function
DOI:
https://doi.org/10.24193/subbmath.2024.4.06Keywords:
Analytic functions, Subordination, Coefficient inequalities, sine function, third Hankel determinant, fourth Hankel determinantAbstract
The objective of this paper is to investigate the bounds of third and fourth Hankel determinants for a generalized subclass of bounded turning functions associated with sine function, in the open unit disc E = {z ∈ C : |z| < 1}. The results are also extended to two-fold and three-fold symmetric functions. This investigation will generalize the results of some earlier works.
Mathematics Subject Classification (2010): 30C45, 30C50, 30C80.
References
1. Altinkaya, Ș., Yalçin, S., Third Hankel determinant for Bazilevic functions, Adv. Math., Sci. J., 5(2016), no. 2, 91-96.
2. Arif, M., Rani, L., Raza, M., Zaprawa, P., Fourth Hankel determinant for the family of functions with bounded turning, Bull. Korean Math. Soc., 55(2018), no. 6, 1703-1711.
3. Arif, M., Raza, M., Tang, H., Hussain, S., Khan, H., Hankel determinant of order three for familiar subsets of analytic functions related to sine function, Open Math., 17(2019), 1615-1630.
4. Babalola, K. O., On H3(1) Hankel determinant for some classes of univalent functions, Inequal. Theory Appl., 6(2010), 1-7.
5. Bieberbach, L., Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, Sitzungsberichte Preussische Akademie der Wissenschaften, 138(1916), 940-955.
6. Bucur, R., Breaz, D., Georgescu, L., Third Hankel determinant for a class of analytic functions with respect to symmetric points, Acta Univ. Apulensis, 42(2015), 79-86.
7. Cho, N.E., Kumar, V., Kumar, S.S., Ravichandran, V., Radius problems for starlike functions associated with sine function, Bull. Iranian Math. Soc., 45(2019), 213-232.
8. De-Branges, L., A proof of the Bieberbach conjecture, Acta Math., 154(1985), 137-152.
9. Ehrenborg, R., The Hankel determinant of exponential polynomials, Amer. Math. Monthly, 107(2000), 557-560.
10. Janteng, A., Halim, S.A., Darus, M., Hankel determinant for starlike and convex functions, Int. J. Math. Anal., 1(2007), no. 13, 619-625.
11. Khan, M.G., Ahmad, B., Sokol, J., Muhammad, Z., Mashwani, W.K., Chinram, R., Petchkaew, P., Coefficient problems in a class of functions with bounded turning associated with sine function, Eur. J. Pure Appl. Math., 14(2021), no. 1, 53-64.
12. Layman, J.W., The Hankel transform and some of its properties, J. Integer Seq., 4(2001), 1-11.
13. Libera, R.J., Zlotkiewiez, E.J., Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc., 85(1982), 225-230.
14. Libera, R.J., Zlotkiewiez, E.J., Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc., 87(1983), 251-257.
15. Ma, W., Generalized Zalcman conjecture for starlike and typically real functions, J. Math. Anal. Appl. 234(1999), 328-329.
16. MacGregor, T.H., Functions whose derivative has a positive real part, Trans. Amer. Math. Soc., 104(1962), 532-537.
17. MacGregor, T.H., The radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 14(1963), 514-520.
18. Mehrok, B.S., Singh, G., Estimate of second Hankel determinant for certain classes of analytic functions, Sci. Magna, 8(2012), no. 3, 85-94.
19. Murugusundramurthi, G., Magesh, N., Coefficient inequalities for certain classes of analytic functions associated with Hankel determinant, Bull. Math. Anal. Appl., 1(2009), no. 3, 85-89.
20. Noor, K.I., Hankel determinant problem for the class of functions with bounded boundary rotation, Rev. Roumaine Math. Pures Appl., 28(1983), no. 8, 731-739.
21. Pommerenke, C., On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., 41(1966), 111-122.
22. Pommerenke, C., Univalent Functions, Math. Lehrbucher, Vandenhoeck and Ruprecht, Gottingen, 1975.
23. Ravichandran, V., Verma, S., Bound for the fifth coefficient of certain starlike functions, Comptes Rendus Math., 353(2015), 505-510.
24. Reade, M.O., On close-to-convex univalent functions, Michigan Math. J., 3(1955-56), 59-62.
25. Shanmugam, G., Stephen, B.A., Babalola, K.O., Third Hankel determinant for α starlike functions, Gulf J. Math., 2(2014), no. 2, 107-113.
26. Singh, G., Hankel determinant for a new subclass of analytic functions, Sci. Magna, 8(2012), no. 4, 61-65.
27. Singh, G., Singh, G., Hankel determinant problems for certain subclasses of Sakaguchi-type functions defined with subordination, Korean J. Math., 30(2022), no. 1, 81-90.
28. Singh, G., Singh, G., Singh, G., Upper bound on fourth Hankel determinant for certain subclass of multivalent functions, Jnanabha, 50(2020), no. 2, 122-127.
29. Singh, G., Singh, G., Singh, G., Fourth Hankel determinant for a subclass of analytic functions defined by generalized Salagean operator, Creat. Math. Inform., 31(2022), no. 2, 229-240.
30. Zhang, H. Y., Tang, H., A study of fourth order Hankel determinant for starlike functions connected with the sine function, J. Funct. Spaces, 2021, Article Id. 9991460, 8 pages.
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