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