The Iteration Scheme with Errors for Zero Point of Maximal Monotone Operator in Hilbert Space
Wei Li · 2006
Let H be a Hilbert space,H→2~H be a maximal monotone operator.It is motivated by the iterative methods for finding the fixed points of non-expansive mappings studied by Mann and Wittmann.Two new iterative algorithms with errors of approximating zero points of maximal monotone operators are given by combining the ideas of Mann's iteration and proximal point iteration.One of the algorithms is proved to be strongly convergent to the zero point of maximal monotone operator and the other is proved to be weakly convergent to it.