An iterative scheme for solving equations with locally $σ$-inverse monotone operators
This work provides a theoretical framework for solving a class of ill-posed nonlinear problems, but it is incremental as it extends existing iterative methods to a specific operator class.
The paper studies an iterative scheme for solving ill-posed nonlinear equations with locally σ-inverse monotone operators, proposing a discrepancy-type stopping rule and proving convergence to the minimal-norm solution.
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.