An inertial iterative algorithm with strong convergence for solving modified split feasibility problem in Banach spaces (Q2036113)

Summary: In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern's iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of \(A^TA\). Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.