Existence and iterative approximation of solutions of a system of general variational inclusions (Q732454)

This paper is devoted to the study of the theory of general variational inclusions in \(q\)-uniformly smooth Banach spaces, using proximal-point mappings. Variational inclusions include variational, quasi-variational, and variational like inequalities as special cases. The interesting problem in this theory is the development of numerical methods which provide an efficient and implementable algorithm for solving variational inclusion and its generalization. Main result: The existence and uniqueness (due to proximal-point mapping technique) of the solution and a suggested Mann type perturbed iterative algorithm for the system of variational inclusions are proved. Convergence criteria and stability of the Mann type perturbed iterative algorithm are discussed. The techniques and results presented in this paper improve the corresponding techniques and results for variational inequalities. One can extend here the obtained results for a system of \(n\)-general variational inclusions.