Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

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Let H be a real Hilbert space and let T:H→2H be 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∈T−10. 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.