Zero theorems of accretive operators (Q624876)

The authors describe an iterative method to find common zeroes of two \(m\)-accretive operators \(A\) and \(B\) on a strictly convex and reflexive Banach space \(X\) with a weakly continuous duality map. Under appropriate assumptions on the parameters and assuming that the operators \(A\) and \(B\) have a common zero, it is shown that the associated iterative process (a version of the modified Mann iteration) converges strongly to a point belonging to the sunny nonexpansive retraction from the collection of all contractive operators on \(\overline{D(A)}\cap \overline{D(B)}\) onto the set of all common zeros of \(A\) and \(B\).