Coefficient Bounds for Al-Oboudi Type Bi-univalent Functions based on a Modified Sigmoid Activation Function and Horadam Polynomials

  • S. R. Swamy Department of Computer Science and Engineering, RV College of Engineering, Bengaluru - 560 059, Karnataka, India
Keywords: Fekete-Szego functional, regular function, MSAF, bi-univalent function, Horodam polynomials

Abstract

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions in $\mathfrak{D}$, an open unit disc, based on $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$, a modified sigmoid activation function (MSAF) and Horadam polynomials. We estimate the initial coefficients bounds for functions of the type $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$ in these families. Continuing the study on the initial cosfficients of these families, we obtain the functional of Fekete-Szeg\"o for each of the two families. Furthermore, we present few interesting observations of the results investigated.

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Published
2021-08-18
How to Cite
Swamy, S. R. (2021). Coefficient Bounds for Al-Oboudi Type Bi-univalent Functions based on a Modified Sigmoid Activation Function and Horadam Polynomials. Earthline Journal of Mathematical Sciences, 7(2), 251-270. https://doi.org/10.34198/ejms.7221.251270
Section
Articles