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 activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) \(k\)-Fibonacci numbers. We derive bounds on initial coefficients Fekete-Szego functional for \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, interesting observations results investigated.