Implicit Set-valued Variational Inclusions in Banach Spaces

In this paper, a new type of variational inclusion named implicit set valued variational inclusion is studied in real Banach spaces. By applications of the method of resolvent operators, equivalence of variational inclusions with resolvent equations is discussed, existence and iterative approximation of solusions of implicit set valued variational inclusions are proved in compact and non compact conditions respectively. With the results presented here, a number of recent results are generalized, improved and unified.