An explicit iteration for zeros of accretive operators

摘要

In this paper, for Lipschitz accretive operator A, an iteration scheme is defined as follows:xn+1=(1-αn)xn+αn(u-βnAxn).Its strong convergence is established for finding some zero of A whenever αn,βn∈(0,1) satisfying conditions:limn→∞αn=0,∑n=1+∞αn=+∞,limn→∞βn=0.Furthermore, some applications for equilibrium problems are given also. In particular, the iteration coefficient is simpler and more general.