Resolvent Operator Linked with - -Mixed Monotone Operator with An Application
The objective of this paper to device the generalized system of nonlinear variational inclusion linked with --mixed monotone operator in Hilbert spaces. First, we give the --mixed monotone operator and defined its resolvent operator. We talk about its single-valued property and Lipschitz continuity. Utilization of resolvent operator approach, we solve the generalized system of nonlinear variational inclusion by given an iterative algorithm concerned with --mixed monotone operator. The consider conditions guaranteed the convergence of iterative sequences obtained by algorithm. Examples are given in support to illustrate the obtained results. This work extend and improve the well-known results in the literature.