A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

For finite difference matrices that are monotone, a discretization error estimate in maximum norm follows from the truncation errors of the discretization. It enables also discretization error estimates for derivatives of the solution. These results are extended to convergent operator splittings of the difference matrix where the major, preconditioning part is monotone but the whole operator is...

In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...