A Self-Adaptive Algorithm for the Common Solution of the Split Minimization Problem and the Fixed Point Problem

In this paper, a new self-adaptive step size algorithm to approximate the solution of split minimization problem and fixed point nonexpansive mappings was constructed, which combined proximal modified Mann’s iterative method with inertial extrapolation. The strong convergence theorem provided in framework Hilbert spaces then proven under some suitable conditions. Our result improved related results literature. Moreover, numerical experiments were also show our algorithm’s consistency, accuracy, performance compared existing algorithms