Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces

Abstract

In this paper, we introduce and study a new class of generalized nonlinear implicit quasi-variational inclusions with general H-monotone operator in Banach spaces. By using the proximal mapping and Nadler’s theorem, we suggest and analyze a class of iterative algorithm for solving the generalized nonlinear implicit quasi-variational inclusion. First, an existence theorem of solutions for the generalized nonlinear implicit quasi-variational inclusion is proved under suitable assumptions. Then, the convergence of the iterative sequences generated by the new algorithm is proved.