A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability

The variational inclusion problems are the generalizations of the variational inequality problems. First, it was noted by Hasounni and Moudafi in 1994. Afterwards, many researchers look into the problems and try to improve the catch, and then the theory of the variational inclusion problems is enriched from time to time. There were some specific ways of solving the systems of the problems and it is called the approximation solvability of the system, which was due to R. U. Verma in 2008. Here in this study, we investigate the approximation solvability of solutions for the system of generalized nonlinear ordered variational inclusions using an iterative algorithm under some apt conditions. We employ the resolvent operator techniques in our iterative scheme as a baseline. Some exceptional cases of the problem and iterative scheme are also discussed.