TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN'S TYPE IN HILBERT SPACES AND APPLICATIONS

Let C be a closed convex subset of a real Hilbert space H. Let A be an inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C. We introduce two iteration schemes of finding a point of (A + B)(-1) 0, where (A + B)(-1) 0 is the set of zero points of A+B. Then, we prove two strong convergence theorems of Halpern's type in a Hilbert space. Using these results, we get new and well-known strong convergence theorems in a Hilbert space.