New approximation-solvability of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators

In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures.

► Generalized resolvent operator technique with (A, ηη, m)-maximal monotonicity is used. ► A class of general nonlinear operator inclusion couples are considered and studied. ► (A, ηη, m)-resolvent operators and relaxed cocoercive type operators are involved. ► We constructed a new perturbed iterative algorithm framework with errors. ► Variational graph convergence analysis for this algorithm framework was investigated.