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{a}l{a}gean type bi-univalent functions by making use of Horadam polynomials involving the modified sigmoid activation function φ(s)=21+e⁻ˢ ,\,s≥0 in the open unit disc D. We investigate the upper bounds on initial coefficients for functions of the form gφ(z)=z+∑ⱼ₌₂∞φ(s)dⱼzʲ, in these newly introduced special families and also discuss the Fekete-Szegö problem. Some interesting consequences of the results established here are also indicated.