Existence Theory for A Kind of Generalized Nonlinear Set-valued Quasi-Variational Inclusionsand Resolvent Equations in Banach Spaces

This paper studied a new set-valued quasi-variational inclusions. By using the properties of m -accretive, the equivalence between the generalized nonlinear set-valued quasi-variational inclusions, the resolvent equations, and the fixed-point problem in Banach spaces are established. Using the equivalence, some iterative algorithms for a new class of generalized nonlinear set-valued quasi-variational inclusions and related optimization problems is developed. The algorithms and results improve and generalize many known corresponding algorithms and results in resent years.