The aim of this paper is to introduce some special families of holomorphic and Sălăgean type bi-univalent functions by making use of Horadam polynomials involving the modified sigmoid activation function ϕ(s) = 2 1+e −s , s ≥ 0 in the open unit disc D. We investigate the upper bounds on initial coefficients for functions of the form g ϕ (z) = z+ ∞ j=2 ϕ(s)d j z 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.