In this paper‚ we explore the aspects of new forms of continuity‚ by utilizing generalized open sets which play a significant role in general topology and real analysis. In this paper we introduced and investigated a relatively new notion of open sets; namely δـeـopen sets. Also, the comparison of this new notion with eـopen sets have been done. Additionally, we apply the notion of δ-e-open sets in topological space to present and study a new classes of functions called δ-e-continuous and contra δ-e-continuous as a new generalization of contra continuity, these functions were compared with e-continuous and contra e-continuous.