CONVERGENCE OF SELF-ADAPTIVE PROJECTION METHODS WITH LINEAR SEARCH FOR PSEUDOMONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

The pseudomonotone variational inequalities and fixed point problems are investigated in Hilbert spaces. We present a self-adaptive projection method with linear search for finding a common solution of the pseudomonotone variational inequalities and fixed points of pseudocontractive operators. We show the strong convergence of the suggested algorithm. Some related corollaries are also given.