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Open Access Research Article

On the fourth Hankel determinant introduced by using a new subclass

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pp. 1043–1057Vol. 28Issue 3-BApril 2025DOI: 10.47974/JIM-2077XML
Received:
08 Oct 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2077
Pages:
1043–1057

Abstract

This article investigates the fourth Hankel determinant for N(α, γ, δ, β, η, λ, μ), the novel subclass for analytic function characterized by subordination. Estimates on a coefficients |ai| with i = 2, 3, 4, 5, 6 and 7  are provided for the functions in this recently described class, as well as an upper limit on fourth Hankel determinant. Authors asserted and demonstrated through the constructing of a new subclass of upper limits for fourth Hankel determinant of subclass for analytic function. A corollaries for main theorems provide some interesting insights, and the accompanying paper highlights the importance of the findings. These results can be used in various applications in mathematics and engineering sciences. For example, system identification, orthogonal polynomials, signal processing, approximation Theory, and this study contributes to the ability to expand our knowledge and understanding for analytical function for unit and its interactive higher relation. These findings are believed to open the doors to explorations and many future applications, not only in mathematics but also in computer science and engineering.

Keywords

Subject Classifications

30C45

References

[1] P. Koebe, “Über die Uniformisierung beliebiger analytischer Kurven,” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, vol. 1907, pp. 191-210 (1907).
[2] P. Duren, “Univalent Functions (Grundlehren der Mathematischen Wissenschaften, 259, Springer-Verlag, New York),” (1983).
[3] S. S. Miller and P. T. Mocanu, Differential subordinations: theory and applications. CRC Press (2000).
[4] S. S. Miller and P. T. Mocanu, “Subordinants of differential superordinations,” Complex variables, vol. 48, no. 10, pp. 815-826 (2003).
[5] R. Mendiratta, S. Nagpal, and V. Ravichandran, “On a subclass of strongly starlike functions associated with exponential function,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 38, pp. 365-386 (2015).
[6] W. Ma, “A unified treatment of some special classes of univalent functions,” in Proceedings of the Conference on Complex Analysis, 1992, 1992: International Press Inc. 
[7] C. Pommerenke, “On the coefficients and Hankel determinants of univalent functions,” Journal of the London Mathematical Society, vol. 1, no. 1, pp. 111-122 (1966).
[8] C. Pommerenke, “On the Hankel determinants of univalent functions,” Mathematika, vol. 14, no. 1, pp. 108-112 (1967).
[9] P. Dienes, “The Taylor series. An introduction to the theory of functions of a complex variable,” Dover Books on Science S (1957).
[10] D. G. Cantor, “Power series with integral coefficients,” (1963).
[11] G. Pólya and I. J. Schoenberg, “Remarks on de la Vallée Poussin means and convex conformal maps of the circle,” (1958).
[12] N. Cho, V. Kumar, S. S. Kumar, and V. Ravichandran, “Radius problems for starlike functions associated with the sine function,” Bulletin of the Iranian Mathematical Society, vol. 45, pp. 213-232 (2019).
[13] A. Janteng, S. A. Halim, and M. Darus, “Coefficient inequality for a function whose derivative has a positive real part,” J. Inequal. Pure Appl. Math, vol. 7, no. 2, pp. 1-5 (2006).
[14] D. V. Krishna and T. RamReddy, “Second Hankel determinant for the class of Bazilevic functions,” Stud. Univ. Babes-Bolyai Math, vol. 60, no. 3, pp. 413-420 (2015).
[15] H. M. Srivastava, Ş. Altınkaya, and S. Yalcın, “Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator,” Filomat, vol. 32, no. 2, pp. 503-516 (2018).
[16] H. M. Srivastava, Q. Z. Ahmad, N. Khan, N. Khan, and B. Khan, “Hankel and Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain,” Mathematics, vol. 7, no. 2, p. 181 (2019).
[17] M. Çağlar, E. Deniz, and H. M. Srivastava, “Second Hankel determinant for certain subclasses ofbi-univalent functions,” Turkish Journal of Mathematics, vol. 41, no. 3, pp. 694-706 (2017).
[18] H. Orhan, N. Magesh, and J. Yamini, “Bounds for the second Hankel determinant of certain bi-univalent functions,” Turkish Journal of Mathematics, vol. 40, no. 3, pp. 679-687 (2016).
[19]  N. H. Shehab and A. R. S. Juma, “Coefficient bounds for certain subclasses for meromorphic functions involving quasi subordination,” in AIP Conference Proceedings, vol. 2400, no. 1: AIP Publishing (2022). 
[20]  N. H. Shehab and A. R. S. Juma, “Quasi subordination of bi-univalent functions involving convolution operator,” in AIP Conference Proceedings, vol. 2398, no. 1: AIP Publishing LLC, p. 060062 (2022). 
[21] N. F. Saray and A. R. S. Juma, “On bi-univalent functions of quasi-subordination associated with convolution operator.”
[22] K. O. Babalola, “On $ H_3 (1) $ Hankel determinant for some classes of univalent functions,” arXiv preprint arXiv:0910.3779 (2009).
[23] N. E. Cho and V. Kumar, “Initial coefficients and fourth Hankel determinant for certain analytic functions,” Miskolc Mathematical Notes, vol. 21, no. 2, pp. 763-779 (2020).
[24] P. Zaprawa, M. Obradović, and N. Tuneski, “Third Hankel determinant for univalent starlike functions,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 115, pp. 1-6 (2021).
[25] E. Doha, “The first and second kind chebyshev coefficients of the moments for the general order derivative on an infinitely differentiable function,” International Journal of Computer Mathematics, vol. 51, no. 1-2, pp. 21-35 (1994).
[26] J. Mason, “Chebyshev polynomial approximations for the L-membrane eigenvalue problem,” SIAM Journal on Applied Mathematics, vol. 15, no. 1, pp. 172-186 (1967).
[27] I. A. R. Rahman, W. G. Atshan, and G. I. Oros, “New concept on fourth Hankel determinant of a certain subclass of analytic functions,” Afrika Matematika, vol. 33, no. 1, p. 7 (2022).
[28] L. R. M. Arif, M. Raza, and P. Zaprawa, “Fourth Hankel determinant for the family of functions with bounded turning,” Bulletin of the Korean Mathematical Society, vol. 55, pp. 1703–1711, Art no. 6 (2018).
[29] M. G. Khan, S. A. Darus, A. A. M. Murad, and A. R. M. Kashfi, “Coefficient problems in a class of functions with bounded turning associated with Sine function,” European Journal of Pure and Applied Mathematics, vol. 14, no. 1, pp. 53-64 (2021).
[30] P. L. Duren, Univalent functions. Springer Science & Business Media (2001).

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