The purpose of this article is to study the split feasibility problem for a countable family of multi-valued k - demicontractive mappings and total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces. In order to solve the problem, we constructed a modified Ishikawas type of algorithm. Under mild conditions, we established convergence theorem using the sequences of the algorithm. The main results presented in the paper improve and extend the recent result of Chang et al. [Applied Mathematics and Computation 219(2013) 10416-10424] , J.N.Ezeora and R.C.Ogbonna[Matematicki Vesnik 70,3(2018),233-242].