Coefficient estimates for starlike and convex functions related to sigmoid functions

  • M. Raza Department of Mathematics, Government College University Faisalabad, Pakistan
  • D. K. Thomas Swansea University, Bay Campus, Swansea, United Kingdom
  • A. Riaz Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Keywords: Analytic functions, starlike, convex, sigmoid function, coefficient bounds, Zalcman functional

Abstract

UDC 517.5

We give sharp coefficient bounds for starlike and convex functions related to modified sigmoid functions. We also provide some sharp coefficients bounds for the inverse  functions and sharp bounds for the initial logarithmic coefficients and  some coefficient differences.

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, N. E. Cho, Logarithmic coefficient bounds and coefficient conjectures for classes associated with convex functions, J. Funct. Spaces, 2021, Article 6690027 (2021). DOI: https://doi.org/10.1155/2021/6690027

K. Bano, M. Raza, D. K. Thomas, On the coefficients of $ B_{1}(alpha)$ Bazilevič functions, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 115, Article 7 (2021). DOI: https://doi.org/10.1007/s13398-020-00947-8

N. E. Cho, S. Kumar, V. Kumar, Hermitian–Toeplitz and Hankel determinants for certain starlike functions, Asian-Eur. J. Math., 15, № 3, Article 2250042 (2022). DOI: https://doi.org/10.1142/S1793557122500425

P. L. Duren, Univalent functions, Berlin, Heidelberg, Springer (1983).

J. E. Brown, A. Tsao, On the Zalcman conjecture for starlike and typically real functions, Math. Z., 191, 467–474 (1986). DOI: https://doi.org/10.1007/BF01162720

P. L. Duren, Coefficients of univalent functions, Bull. Amer. Math. Soc. (5), 83, 891–911 (1977). DOI: https://doi.org/10.1090/S0002-9904-1977-14324-3

P. Goel, S. S. Kumar, Certain class of starlike functions associated with modified sigmoid function, Bull. Malays. Math. Sci. Soc., 43, 957–991 (2020). DOI: https://doi.org/10.1007/s40840-019-00784-y

M. G. Khan, B. Ahmad, G. Murugusundaramoorthy, R. Chinram, W. K. Mashwani, Applications of modified sigmoid functions to a class of starlike functions, J. Funct. Spaces, 2020, Article ID 8844814 (2020). DOI: https://doi.org/10.1155/2020/8844814

W. Ma, D. Minda, A unified treatment of some special classes of univalent functions, Proc. Conf. Complex Analysis, Z. Li, F. Ren, L. Yang, S. Zhang (Eds), Int. Press (1994), p.~157–169.

D. V. Prokhorov, J. Szynal, Inverse coefficients for $(alpha,beta )$-convex functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 35, 125–143 (1981).

V. Ravichandran, S. Verma, Bound for the fifth coefficient of certain starlike functions, C. R. Math. Acad. Sci. Paris, 353, 505–510 (2015). DOI: https://doi.org/10.1016/j.crma.2015.03.003

Y. J. Sim, D. K. Thomas, A note on spirallike functions, Bull. Aust. Math. Soc., 105, № 1, 117–123 (2022). DOI: https://doi.org/10.1017/S0004972721000198

Y. J. Sim, D. K. Thomas, On the difference of inverse coefficients of univalent functions, Symmetry, 12, № 12 (2020). DOI: https://doi.org/10.3390/sym12122040

A. Vasudevarao, A. Pandey, The Zalcman conjecture for certain analytic and univalent functions, J. Math. Anal. and Appl., 492, № 2 (2020). DOI: https://doi.org/10.1016/j.jmaa.2020.124466

Published
24.05.2023
How to Cite
RazaM., ThomasD. K., and RiazA. “Coefficient Estimates for Starlike and Convex Functions Related to Sigmoid Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 5, May 2023, pp. 683 -97, doi:10.37863/umzh.v75i5.7093.
Section
Research articles