An iterative scheme for solving equations with locally $σ$-inverse monotone operators

Abstract

An iterative scheme for solving ill-posed nonlinear equations with locally $σ$-inverse monotone operators is studied in this paper. A stopping rule of discrepancy type is proposed. The existence of $u_{n_δ}$ satisfying the proposed stopping rule is proved. The convergence of this element to the minimal-norm solution is justified mathematically.