Approximating solutions of maximal monotone operators in Hilbert spaces

Let H he a real Hilbert space and let T:H --> 2(H) he a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit v epsilon T(-1)0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration. (C) 2000 Academic Press.