A contraction proximal point algorithm with two monotone operators

It is a known fact that the method of alternating projections introduced long ago by
von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets
of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two
maximal monotone operators is introduced and strong convergence results associated with it are
proved. For the case when the two operators are subdifferentials of indicator functions, this new
algorithm coincides with the old method of alternating projections. Several other important algorithms,
such as the contraction proximal point algorithm, occur as special cases of our algorithm.
Hence our main results generalize and unify many results that occur in the literature.