General system of (A,η)(A,η)-monotone variational inclusion problems based on generalized hybrid iterative algorithm

First a new system of nonlinear set-valued variational inclusions involving (A,η)(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)(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.