We give sharp coefficient bounds for starlike and convex functions related to modified sigmoid functions. We also provide some sharp coefficient bounds for the inverse functions and sharp bounds for the initial logarithmic coefficients and some coefficient differences.
Similar content being viewed by others
References
R. M. Ali, “Coefficients of the inverse of strongly starlike functions,” Bull. Malays. Math. Sci. Soc., 26, 63–71 (2003).
D. Alimohammadi, E. A. Adegani, T. Bulboacă, and N. E. Cho, “Logarithmic coefficient bounds and coefficient conjectures for classes associated with convex functions,” J. Funct. Spaces, 2021, Article 6690027 (2021).
K. Bano, M. Raza, and D. K. Thomas, “On the coefficients of B1(α) Bazilevič functions,” Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 115, Article 7 (2021).
N. E. Cho, S. Kumar, and V. Kumar, “Hermitian–Toeplitz and Hankel determinants for certain starlike functions,” Asian-Europ. J. Math., 15, No. 3, Article 2250042 (2022).
P. L. Duren, Univalent Functions, Springer, Berlin–Heidelberg, (1983).
J. E. Brown and A. Tsao, “On the Zalcman conjecture for starlike and typically real functions,” Math. Z., 191, 467–474 (1986).
P. L. Duren, “Coefficients of univalent functions,” Bull. Amer. Math. Soc. (5), 83, 891–911 (1977).
P. Goel and S. S. Kumar, “Certain class of starlike functions associated with modified sigmoid function,” Bull. Malays. Math. Sci. Soc., 43, 957–991 (2020).
M. G. Khan, B. Ahmad, G. Murugusundaramoorthy, R. Chinram, and W. K. Mashwani, “Applications of modified sigmoid functions to a class of starlike functions,” J. Funct. Spaces, 2020, Article ID 8844814 (2020).
W. Ma and D. Minda, “A unified treatment of some special classes of univalent functions,” Proc. Conf. on Complex Analysis, Z. Li, F. Ren, L. Yang, S. Zhang (Eds.), Int. Press (1994), pp. 157–169.
D. V. Prokhorov and J. Szynal, “Inverse coefficients for (α, β)-convex functions,” Ann. Univ. Mariae Curie-Sklodowska, Sec. A, 35, 125–143 (1981).
V. Ravichandran and S. Verma, “Bound for the fifth coefficient of certain starlike functions,” C. R. Math. Acad. Sci. Paris, 353, 505–510 (2015).
Y. J. Sim and D. K. Thomas, “A note on spirallike functions,” Bull. Austral. Math. Soc., 105, No. 1, 117–123 (2022).
Y. J. Sim and D. K. Thomas, “On the difference of inverse coefficients of univalent functions,” Symmetry, 12, No. 12 (2020).
A. Vasudevarao and A. Pandey, “The Zalcman conjecture for certain analytic and univalent functions,” J. Math. Anal. Appl., 492, No. 2 (2020).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 683–697, May, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i5.7093.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Raza, M., Thomas, D.K. & Riaz, A. Coefficient Estimates for Starlike and Convex Functions Related to Sigmoid Functions. Ukr Math J 75, 782–799 (2023). https://doi.org/10.1007/s11253-023-02228-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-023-02228-0