## New perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi-variational inclusions.(English)Zbl 1207.65088

Summary: This paper introduces a new system of extended generalized nonlinear mixed quasi-variational inclusions involving $$A$$-maximal $$m$$-relaxed $$\eta$$-accretive (so called $$(A,\eta )$$-accretive; [H.-Y. Lan et al., Comput. Math. Appl. 51, No. 9-10, 1529–1538 (2006; Zbl 1207.49011)]) mappings in $$q$$-uniformly smooth Banach spaces. By using the resolvent operator technique for $$A$$-maximal $$m$$-relaxed $$\eta$$-accretive mappings due to Lan et al., we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi-variational inclusions and construct a new perturbed $$N$$-step iterative algorithm with mixed errors for solving the mentioned system. We also prove the convergence of the sequences generated by our algorithms in $$q$$-uniformly smooth Banach spaces. The results presented in this paper extend and improve some known results in the literature.

### MSC:

 65K15 Numerical methods for variational inequalities and related problems 47J20 Variational and other types of inequalities involving nonlinear operators (general) 47J25 Iterative procedures involving nonlinear operators 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Zbl 1207.49011
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