An iterative algorithm for solving generalized variational inequality problems and fixed point problems
Kai Tu, Fu-quan Xia, Jen‐Chih Yao · Applicable Analysis · 2015
We propose an iterative scheme for finding a common element of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem in Euclidean space . Under some mild conditions, we establish the convergence theorem for the proposed algorithm. We also give a suitable condition to ensure the intersection of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem to be nonempty. In addition, under certain error bound conditions, we prove the convergence rate of the iterative sequence. Preliminary computational experience is also reported.