Some special families of holomorphic and Sălăgean type bi-univalent functions associated with Horadam polynomials involving a modified sigmoid activation function

The aim of this paper is to introduce some special families holomorphic and S\u{a}l\u{a}gean type bi-univalent functions by making use Horadam polynomials involving the modified sigmoid activation function $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$ in open unit disc $\mathfrak{D}$. We investigate upper bounds on initial coefficients for form $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$, these newly introduced also discuss Fekete-Szegö problem. Some interesting consequences results established here are indicated.