A self-adaptive relaxed primal-dual iterative algorithm for solving the split feasibility and the fixed point problem

In this paper, we introduce a new numerical simulation iterative algorithm to solve the split feasibility problem and the fixed point problem with demicontractive mappings. Ou r algorithm mainly involves primal-dual iterative, relaxed projection, inertial technique and self-adaptive step size. Under reasonable conditions, the strong convergence of ou r algorithm is established. Moreover, we provide some numerical simulation examples to demonstrate the efficiency of ou r iterative algorithm compared to existing algorithms in the other literature.