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

Abstract

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with the activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) and \(k\)-Fibonacci numbers. We derive the bounds on initial coefficients and the Fekete-Szego functional for functions of the type \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, we present interesting observations of the results investigated.