General system of [formula omitted]-monotone variational inclusion problems based on generalized hybrid iterative algorithm

Abstract

First a new system of nonlinear set-valued variational inclusions involving ( A , η ) -monotone mappings in Hilbert spaces is introduced and then its solvability is explored. Based on the general resolvent operator method associated with ( A , η ) -monotone mappings, approximation solvability of this system of nonlinear set-valued variational inclusions is established. The convergence analysis is discussed in detail. The obtained results generalize a number of results on nonlinear variational inclusion systems.