The purpose of this paper is by using the shrinking projection method to
introduce and study an iterative process to approximate a common
solution of split variational inclusion problem and fixed point problem
for an asymptotically nonexpansive semigroup in real Hilbert spaces.
Further, we prove that the sequences generated by the proposed iterative
method converge strongly to a common solution of split variational
inclusion problem and fixed point problem for an asymptotically
nonexpansive semigroup. As applications, we shall utilize the results to
study the split optimization problem and the split variational
inequality.