A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces

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.