The Convergence of Iterative Methed for Families of Nonexpansive Mappings and Monotone Mappings
WU Ding-ping · Journal of Chengdu University of Information Technology · 2013
Based on the terative algorithm of a nonexpansive mapping and a monotone mapping in Hilbert spaces given by Yonghong Yao etc,under the situation that currently less iterative method between nonexpansive mapping families and other mappings are studied,integrating the iterative algorithm for families of nonexpansive mappings in Hilbert spaces given by Tomoo Shimizu etc,we introduce a new iterative scheme of nonexpansive families mappings and α-inverse-strongly monotone mappings.Through the establishment of a strong convergence theorem and by using the new iterative algorithm,we got the common element of the set of fixed points of families of nonexpansive mappings and the set of solutions of the variational for α-inverse-strongly monotone mappings.The results show that the iterative scheme converges strongly to the common element.