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

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions in D, an open unit disc, based on φ(s)=21+e⁻ˢ ,\,s≥0, a modified sigmoid activation function (MSAF) and Horadam polynomials. We estimate the initial coefficients bounds for functions of the type gφ(z)=z+∑ⱼ₌₂∞φ(s)dⱼzʲ 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.