An Algorithm to Solve the Variational Inequality Problem Based on the Common Solutions of Two Classes of Problems
We study a new algorithm to solve a common solution of the split fea-sibility problem and the fixed point problem involving quasi-nonexpansive mappings in Hilbert spaces.Based on the common solutions of these two classes of problems,we solve the variational inequality problem.Compared with the predecessors,the self-adaptive technique and the inertial iteration method are added,which can speed up the convergence rate of the iterative sequence generated by our algorithms.At the same time,we extend the involving previous nonexpansive mappings to extensive quasi-nonexpansive mappings.In addition,a strong positive bounded operator is added to the algorithm,which extends the original viscous iterative algorithm to a more general viscous iterative algorithm.The effectiveness of the algorithm is verified by numerical examples.
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