Summary: This paper deals with the split feasibility problem that requires to find a point closest to a closed convex set in one space such that its image under a linear transformation will be closest to another closed convex set in the image space. By combining perturbed strategy with inertial technique, we construct an inertial perturbed projection algorithm for solving the split feasibility problem. Under some suitable conditions, we show the asymptotic convergence. The results improve and extend the algorithms presented by C. Byrne
[Inverse Probl. 18, No. 2, 441–453 (2002; Zbl 0996.65048
)] and by J. Zhao
and Q. Yang
[Inverse Probl. 21, No. 5, 1791–1799 (2005; Zbl 1080.65035
)] and the related convergence theorem.