Approximating zero points of accretive operators by an implicit iterative sequences in Banach spaces

In this paper, we introduce an implicit iterative sequence to approximate zero points of accretive operators in Banach spaces and then prove weak convergence theorems for resolvents of accretive operators in Banach spaces satisfying Opial's condition. Further, we discuss the strong convergence of the iterative sequences for resolvents of accretive operators with compact domains in general Banach spaces. Using these results, we consider the variational inequality problem of finding a solution of a variational inequality.