Coefficient bounds for Al-Oboudi type bi-univalent functions connected with a modified sigmoid activation function and k -Fibonacci numbers

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with the activation function \(% φ (s)=\ 2/(1+e⁻ˢ),\,s∈ R\) and \(k\)-Fibonacci numbers. We derive the bounds on initial coefficients and the Fekete-Szego functional for functions of the type \(gφ(z)=z+∑ ⱼ₌₂∞φ (s)dⱼzʲ\) in these introduced families. Furthermore, we present interesting observations of the results investigated.