We introduce a class of η -accretive mappings in a real Banach space and show that the η -proximal point mapping for η - m -accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving η -accretive mappings in real Banach space, and discuss its convergence criteria. The class of η -accretive mappings includes several important classes of operators that have been studied by various authors.