A New Perturbed Iterative Algorithm with Mixed Errors for Solving System of Generalized Nonlinear Variational Inclusions
A new system of generalized nonlinear variational inclusions with A-maximal m-relaxed eta-accretive (so called (A,eta)-accretive [22]) mappings in q-uniformly smooth Banach spaces is introduced and studied. By using the resolvent operator technique associated with A-maximal m-relaxed eta-accretive mappings due to Lan et al., the existence and uniqueness, of solution for this system of generalized nonlinear variational inclusions is verified and a new perturbed iterative algorithm with mixed errors for solving the aforementioned system is constructed. Also the convergence of the sequences generated by the our algorithm in q-uniformly smooth Banach spaces is proved. The results presented in this paper extend and improve some known results in the literature.
perturbed iterative algorithm with mixed errors a-maximal m-relaxed eta-accretive resolvent operator technique a system of generalized nonlinear variational inclusions variational convergence