Abstract
In this paper, we study some properties of A -monotone operator in Banach space, give the notion of proximal mapping associated with the A -monotone operator and show its Lipschitz continuity. We also consider a new system of generalized nonlinear quasi-variational-like inclusions with A -monotone operators in Banach spaces and constructed a new iterative algorithm for solving the system of generalized nonlinear quasi-variational-like inclusions in Banach spaces. Under suitable assumptions, we prove the convergence of the iterative sequences generated by the algorithm.
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