New System of Quasi-variational-Like Inclusions Involving Monotone Operators in General Banach Spaces

A new system of set-valued quasi-variational-like inclusions (in short, QVLI) involving H-n-monotone operators is introduced and studied in general Banach spaces without uniform smoothness. Moreover, A new iterative algorithm to find the approximation solutions of the QVLI is suggested and analyzed. It is proved that the iterative sequences generated by the algorithm converge strongly to the exact solution of the QVLI under suitable assumptions. These new results extend and improve the corresponding ones in this field.