On inertial non-lipschitz stepsize algorithms for split feasibility problems

In this paper, we introduce a Non-Lipschitz stepsize strategy, new parameters and inertial effects in projection and contraction approaches to solve split feasibility problems in real Hilbert spaces. Weak and strong convergence theorems for our methods are established with non-Lipschitz continuity and expansiveness of the monotone operator and related projection mappings, respectively. Further, we discuss a nonasymptotic O(1/n) convergence rate for the proposed algorithms. Finally, signal recovery and image deblurring problems that we provide for demonstration and comparison.