A Certain Class of Function Analytic and Subordinate to the Modified Sigmoid Function

  • Ezugorie Obiageri M. Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
  • Ishiaku Z. Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
  • Fadipe-Joseph Olubunmi A. Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
Keywords: analytic function, univalent function, integral operator, special function, starlikeness convexity

Abstract

A certain class of functions, analytic and subordinate to the modified sigmoid function, is defined. Coefficient inequalities, Toeplitz, distortion, and Fekete-Szegö problems of this class were investigated. It was observed that the results obtained provide extensions to many known results in geometric function theory. Special cases of the results were equally highlighted.

References

Duren, P. L. (1983). Univalent functions. Springer-Verlag.

Elumalai, M., & Abbas, K. W. (2025). Coefficient estimates for two new subclasses of bi-valent functions involving Laguerre polynomial. Earthline Journal of Mathematical Sciences, 15(2), 187–199. https://doi.org/10.34198/ejms.15225.187199

Ezeafulukwe, U. A., Maslina, D., & Olubunmi, A. F. (2018). On analytic properties of a sigmoid function. International Journal of Mathematics and Computer Science, 2, 187–199.

Fadipe-Joseph, O. A., Oladipo, A. T., & Ezeafulukwe, U. A. (2013). Modified sigmoid function in univalent function theory. International Journal of Mathematical Sciences and Engineering Application, 7, 313–317.

Fitri, S., Thomas, D. K., & Wibowo, R. B. E. (2020). Some coefficient inequalities of Bazilevic functions in a sector. Indian Journal of Mathematics, 62(2), 191–202.

Jahangiri, M. (1986). On coefficient of powers of a class of Bazilevic functions. Indian Journal of Pure and Applied Mathematics, 17(9), 1140–1144.

Karthikeyan, K. R., Murugusundaramorthy, G., & Cho, N. E. (2021). Some inequality on Bazilevic class of functions involving quasi-subordination. AIMS Mathematics, 6(7), 7111–7124. https://doi.org/10.3934/math.2021417

Shi, L., Srivastava, H. M., Arif, M., Hussain, S., & Khan, H. (2019). An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential function. Symmetry, 11(5), 598. https://doi.org/10.3390/sym11050598

Libera, R. J., & Zlotkiewicz, E. J. (1983). Coefficient bounds for the inverse of a function with derivative in R. Proceedings of the American Mathematical Society, 87(2), 251–257. https://doi.org/10.2307/2043698

Made Asih, S., Fitri, S., Wibowo, R. B. E., & Marjono. (2023). Hankel determinant and Toeplitz determinant on the class of Bazilevic function related to the Bernoulli Lemniscate. European Journal of Pure and Applied Mathematics, 16, 1290–1301. https://doi.org/10.29020/nybg.ejpam.v16i2.4772

Marjono. (2017). Subordination of analytic functions. The Australian Journal of Mathematical Analysis and Applications, 14, 1–5.

Marjono. (2006). On subclass of Bazilevic function B₁(α), its distortion and the Fekete-Szegö problem. Journal of Mathematics and Its Applications, 3(1), 1–10. https://doi.org/10.12962/j1829605X.v3i1.1391

Mohsan, R., & Khalida, I. N. (2020). Subclass of Bazilevic functions of complex order. AIMS Mathematics, 5(3), 2448–2460. https://doi.org/10.3934/math.2020162

Murat, C., Ismaila, O. I., Timilehin, G., & Abbas, K. W. (2024). Toeplitz determinants for lambda-pseudo-starlike functions. Communications of the Korean Mathematical Society, 39(3), 647–655.

Pommerenke, C., & Jensen, G. (1975). Univalent functions. Vandenhoeck & Ruprecht.

Umar, S., Mohammed, A., Mohsan, R., & See, K. L. (2020). On a subclass related to Bazilevic functions. AIMS Mathematics, 5(3), 2040–2056. https://doi.org/10.3934/math.2020135

Shell-Small, T. (1972). On Bazilevic functions. Quarterly Journal of Mathematics, Oxford Series, 2(23), 135–142. https://doi.org/10.1093/qmath/23.2.135

Singh, R. (1973). On Bazilevic functions. Proceedings of the American Mathematical Society, 38, 261–271.

Thomas, D. K., & Abdul Halim, S. (2017). Toeplitz matrices whose elements are the coefficients of starlike and close-to-convex functions. Bulletin of the Malaysian Mathematical Society, 40, 1781–1790. https://doi.org/10.1007/s40840-016-0385-4

Thomas, D. K. (1985). On a subclass of Bazilevic functions. International Journal of Mathematical Sciences, 8(4), 779–783. https://doi.org/10.1155/S0161171285000850

Published
2025-05-06
How to Cite
Ezugorie Obiageri M., Ishiaku Z., & Fadipe-Joseph Olubunmi A. (2025). A Certain Class of Function Analytic and Subordinate to the Modified Sigmoid Function. Earthline Journal of Mathematical Sciences, 15(4), 639-647. https://doi.org/10.34198/ejms.15425.639647
Section
Articles