The aim of our paper is to introduce generalized neighborhood bases and \(gn-T_2\)-spaces. \((\psi, \psi’)\)-continuity, sequentially \((\psi, \psi’)\)-continuity, and \(\psi\)-convergency are investigated on strong generalized first countable spaces, and also two results about \(\psi\)-convergency on \((\psi, \psi’)\)-\(T_2\)-spaces are given.