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Keywords:
analytic function; univalent function; Hankel determinant; upper bound; bounded turning
analytic function; univalent function; Hankel determinant; upper bound; bounded turning
Summary:
We improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning.
References:
[1] Ali, R. M.: On a subclass of starlike functions. Rocky Mt. J. Math. 24 (1994), 447-451. DOI 10.1216/rmjm/1181072410 | MR 1277337 | Zbl 0816.30010
[2] Bansal, D., Maharana, S., Prajapat, J. K.: Third order Hankel determinant for certain univalent functions. J. Korean Math. Soc. 52 (2015), 1139-1148. DOI 10.4134/JKMS.2015.52.6.1139 | MR 3418550 | Zbl 1328.30005
[3] Carlson, F.: Sur les coefficients d'une fonction bornée dans le cercle unité. Ark. Mat. Astron. Fys. A27 (1940), 8 pages French. MR 0003231 | Zbl 0023.04905
[4] Dienes, P.: The Taylor Series: An Introduction to the Theory of Functions of a Complex Variable. Dover Publications, New York (1957). MR 0089895 | Zbl 0078.05901
[5] Grenander, U., Szegő, G.: Toeplitz Forms and Their Applications. California Monographs in Mathematical Sciences. University of California Press, Berkeley (1958). MR 0094840 | Zbl 0080.09501
[6] Hayman, W. K.: On the second Hankel determinant of mean univalent functions. Proc. Lond. Math. Soc., III. Ser. 18 (1968), 77-94. DOI 10.1112/plms/s3-18.1.77 | MR 0219715 | Zbl 0158.32101
[7] Janteng, A., Halim, S. A., Darus, M.: Coefficient inequality for a function whose derivative has a positive real part. JIPAM, J. Inequal. Pure Appl. Math. 7 (2006), Article ID 50, 5 pages. MR 2221331 | Zbl 1134.30310
[8] Janteng, A., Halim, S. A., Darus, M.: Hankel determinant for starlike and convex functions. Int. J. Math. Anal., Ruse 1 (2007), 619-625. MR 2370200 | Zbl 1137.30308
[9] Khatter, K., Ravichandran, V., Kumar, S. S.: Third Hankel determinant of starlike and convex functions. J. Anal. 28 (2020), 45-56. DOI 10.1007/s41478-017-0037-6 | MR 4077300 | Zbl 1435.30049
[10] Kowalczyk, B., Lecko, A., Sim, Y. J.: The sharp bound of the Hankel determinant of the third kind for convex functions. Bull. Aust. Math. Soc. 97 (2018), 435-445. DOI 10.1017/S0004972717001125 | MR 3802458 | Zbl 1394.30007
[11] Krzyz, J.: A counter example concerning univalent functions. Folia Soc. Sci. Lublin. Mat. Fiz. Chem. 2 (1962), 57-58.
[12] Obradović, M., Tuneski, N.: Hankel determinant of second order for some classes of analytic functions. Available at https://arxiv.org/abs/1903.08069 (2019), 6 pages. MR 4392540
[13] Obradović, M., Tuneski, N.: New upper bounds of the third Hankel determinant for some classes of univalent functions. Available at https://arxiv.org/abs/1911.10770 (2020), 10 pages. MR 4198419
[14] Thomas, D. K., Tuneski, N., Vasudevarao, A.: Univalent Functions: A Primer. De Gruyter Studies in Mathematics 69. De Gruyter, Berlin (2018). DOI 10.1515/9783110560961 | MR 3791816 | Zbl 1397.30002
[15] Krishna, D. Vamshee, Venkateswarlu, B., RamReddy, T.: Third Hankel determinant for bounded turning functions of order alpha. J. Niger. Math. Soc. 34 (2015), 121-127. DOI 10.1016/j.jnnms.2015.03.001 | MR 3512016 | Zbl 1353.30013
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