Cai, Tao; Wang, Li; Cho, Min-Hyung; Kang, Shin Min Approximation-solvability of a system of generalized variational inequalities in Banach spaces. (English) Zbl 1235.47059 Int. J. Pure Appl. Math. 71, No. 3, 441-453 (2011). Summary: In this paper, we introduce a new system of generalized variational inequalities and two concepts of \(\eta\)-subdifferential and \(A\)-\(\eta\)-proximal mappings of a proper functional in Banach spaces and prove the existence and Lipschitz continuity of an \(A\)-\(\eta\)-proximal mapping of a lower semicontinuous \(\eta\)-subdifferentiable proper functional in reflexive Banach spaces. We suggest a new iterative algorithm for computing the approximate solutions of a system of generalized variational inequalities. Under certain conditions, we establish the existence of solutions and convergence of the iterative algorithm for the system of generalized variational inequalities. MSC: 47J20 Variational and other types of inequalities involving nonlinear operators (general) 49J40 Variational inequalities 47J25 Iterative procedures involving nonlinear operators 65J15 Numerical solutions to equations with nonlinear operators Keywords:\(A\)-\(\eta\)-proximal mapping; system of generalized variational inequalities; Banach space PDFBibTeX XMLCite \textit{T. Cai} et al., Int. J. Pure Appl. Math. 71, No. 3, 441--453 (2011; Zbl 1235.47059) Full Text: Link