Coefficients Estimates for a Subclass of Starlike Functions
Abstract
The paper mainly investigates the initial coefficients for the subclasses of starlike functions defined by using the Cosine function involving $\alpha$ ($0\leq\alpha<1$), we obtain upper bounds for initial order of Hankel determinants and symmetric Toeplitz determinants whose elements are the initial coefficients. Also, we obtain initial coefficient estimation of logarithmic coefficients for the subclass.
References
Ahuja, O. P., Khatter, K., & Ravichandran, V. (2021). Toeplitz determinants associated with Ma-Minda classes of starlike and convex functions. Iranian Journal of Science and Technology, Transactions A: Science, 45(6), 2021-2027. https://doi.org/10.1007/s40995-021-01173-6
Ali, M. F., Thomas, D. K., & Vasudevarao, A. (2018). Toeplitz determinants whose elements are the coefficients of analytic and univalent functions. Bulletin of the Australian Mathematical Society, 97(2), 253-264. https://doi.org/10.1017/S0004972717001174
Ali, M. F., & Vasudevarao, A. (2018). On logarithmic coefficients of some close-to-convex functions. Proceedings of the American Mathematical Society, 146(3), 1131-1142. http://dx.doi.org/10.1090/proc/13817
Allu, V., Lecko, A., & Thomas, D. K. (2022). Hankel, Toeplitz, and Hermitian-Toeplitz determinants for certain close-to-convex functions. Mediterranean Journal of Mathematics, 19(1), Paper No. 22, 17 pp. https://doi.org/10.1007/s00009-021-01934-y
Allu, V., Arora, V., & Shaji, A. (2023). On the second Hankel determinant of logarithmic coefficients for certain univalent functions. Mediterranean Journal of Mathematics, 20(2), Paper No. 81, 10 pp. https://doi.org/10.1007/s00009-023-02272-x
Cho, N. E., Kowalczyk, B., Kwon, O. S., Lecko, A., & Sim, Y. J. (2020). On the third logarithmic coefficient in some subclasses of close-to-convex functions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 114(2), Paper No. 52, 14 pp. https://doi.org/10.1007/s13398-020-00786-7
Cho, N. E., Kumar, V., Kumar, S. S., & Ravichandran, V. (2019). Radius problems for starlike functions associated with the sine function. Bulletin of the Iranian Mathematical Society, 45(1), 213-232. https://doi.org/10.1007/s41980-018-0127-5
Duren, P. (1983). Univalent functions. Springer-Verlag, New York Inc.
Futa, A., Jastrzebska, M., & Zaprawa, P. (2023). Bounds of the third and the fourth logarithmic coefficients for close-to-convex functions. Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science, 24(3), 205-216. https://doi.org/10.59277/PRA-SER.A.24.3.01
Giri, S., & Kumar, S. S. (2023). Toeplitz determinants for a class of holomorphic mappings in higher dimensions. Complex Analysis and Operator Theory, 17(6), Paper No. 86, 16 pp. https://doi.org/10.1007/s11785-023-01394-0
Kazimoglu, S., Deniz, E., & Srivastava, H. M. (2024). Sharp coefficients bounds for starlike functions associated with Gregory coefficients. Complex Analysis and Operator Theory, 18(1), Paper No. 6, 19 pp. https://doi.org/10.1007/s11785-023-01445-6
Kowalczyk, B., & Lecko, A. (2022). Second Hankel determinant of logarithmic coefficients of convex and starlike functions. Bulletin of the Australian Mathematical Society, 105(3), 458-467. https://doi.org/10.1017/S0004972721000836
Kowalczyk, B., & Lecko, A. (2023). The second Hankel determinant of the logarithmic coefficients of strongly starlike and strongly convex functions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 117(2), Paper No. 91, 13 pp. https://doi.org/10.1007/s13398-023-01427-5
Mandal, S., & Ahamed, M. B. (2024). Second Hankel determinant of logarithmic coefficients of inverse functions in certain classes of univalent functions. Lithuanian Mathematical Journal, 64(1), 67-79. https://doi.org/10.1007/s10986-024-09623-5
Obradovic, M., Ponnusamy, S., & Wirths, K.-J. (2018). Logarithmic coefficients and a coefficient conjecture for univalent functions. Monatshefte für Mathematik, 185(3), 489-501. https://doi.org/10.1007/s00605-017-1024-3
Pommerenke, Ch. (1966). On the coefficients and Hankel determinants of univalent functions. Journal of the London Mathematical Society, 41, 111-122. https://doi.org/10.1112/jlms/s1-41.1.111
Pommerenke, Ch. (1975). Univalent Functions. Vandenhoeck & Ruprecht, Gottingen.
Ponnusamy, S., Sharma, N. L., & Wirths, K.-J. (2018). Logarithmic coefficients of the inverse of univalent functions. Results in Mathematics, 73(4), Paper No. 160, 20 pp. https://doi.org/10.1007/s00025-018-0921-7
Ponnusamy, S., & Sugawa, T. (2021). Sharp inequalities for logarithmic coefficients and their applications. Bulletin des Sciences Mathématiques, 166, Paper No. 102931, 23 pp. https://doi.org/10.1016/j.bulsci.2020.102931
Raza, M., Riaz, A., & Thomas, D. K. (2024). The third Hankel determinant for inverse coefficients of convex functions. Bulletin of the Australian Mathematical Society, 109(1), 94-100. https://doi.org/10.1017/S0004972723000357
Srivastava, H. M., Shaba, T. G., Ibrahim, M., Tchier, F., & Khan, B. (2024). Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials. Bulletin des Sciences Mathématiques, 192, Paper No. 103405, 17 pp. https://doi.org/10.1016/j.bulsci.2024.103405
Srivastava, H. M., Rath, B., Kumar, K. S., & Krishna, D. V. (2024). Some sharp bounds of the third-order Hankel determinant for the inverses of the Ozaki type close-to-convex functions. Bulletin des Sciences Mathématiques, 191, Paper No. 103381, 19 pp. https://doi.org/10.1016/j.bulsci.2023.103381
Tang, H., Srivastava, H. M., Li, S. H., & Deng, G. T. (2020). Majorization results for subclasses of starlike functions based on the sine and cosine functions. Bulletin of the Iranian Mathematical Society, 46(2), 381-388. https://doi.org/10.1007/s41980-019-00262-y
Thomas, D. K. (2016). On the logarithmic coefficients of close to convex functions. Proceedings of the American Mathematical Society, 144(4), 1681-1687. https://doi.org/10.1090/proc/12921
Wanas, A. K., & Majeed, A. M. (2021). Second Hankel determinant for a certain subclass of λ-pseudo-starlike bi-univalent functions. Iranian Journal of Mathematical Sciences and Informatics, 16(2), 49-59. https://doi.org/10.52547/ijmsi.16.2.49
Wanas, A. K., & Sokół, J. (2021). Second Hankel determinant for analytic and bi-univalent functions with respect to symmetric conjugate. Analele Universității din Oradea, Fascicula Matematică, 28(1), 125-134.
Wang, D. R., Huang, H. Y., & Long, B. Y. (2021). Coefficient problems for subclasses of close-to-star functions. Iranian Journal of Science and Technology, Transactions A: Science, 45(3), 1071-1077. https://doi.org/10.1007/s40995-021-01115-2
Wang, Z. G., Hussain, M., & Wang, X. Y. (2023). On sharp solutions to majorization and Fekete-Szegö problems for starlike functions. Miskolc Mathematical Notes, 24(2), 1003-1019. https://doi.org/10.18514/MMN.2023.3986
Wang, Z. G., Srivastava, H. M., Arif, M., Liu, Z. H., & Ullah, K. (2024). Sharp bounds on Hankel determinants of bounded turning functions involving the hyperbolic tangent function. Applicable Analysis and Discrete Mathematics. https://doi.org/10.2298/AADM221203013W
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