We introduce a genuine summation-integral type operators based on Lupaş-Jain type base functions related to the unbounded sequences. We investigated their degree of approximation in terms of modulus of continuity and $\mathcal{K}$-functional for the functions from bounded and continuous functions space. Furthermore, we give some theorems for the local approximation properties of functions belonging to Lipschitz class. Also, we give Voronovskaja theorem for these operators.