Based on the recent important result of S. S. Chang, H. W. Joseph Lee, C. K. Chan, L. Wang, L.J. Qin [Appl. Math. Comput. 219 (2013) 10416--10424], we study in this article the split feasibility problem for a countable family of multi-valued $\kappa-$strictly pseudo-contractive mappings and total asymptotically strict pseudo-contractive mappings in infinite dimensional Hilbert spaces. The main results presented in this paper improve and extend the aforementioned result.