On fixed point algorithms for solving split inverse problems with applications

Abstract

We study a certain class of split inverse problems which includes many other split-type problems. We propose a new inertial Mann-type Tseng's extragradient method to approximate the solution of this problem in real Hilbert spaces. Strong convergence of the proposed scheme to a minimum-norm solution of the problem is established when the associated single-valued operators are monotone and uniformly continuous with self-adaptive step size strategy. Moreover, we also study some classes of split inverse problems and provide some numerical implementations to illustrate our method and compare with a non-inertial version and a recently related method.