TWO NEW MODIFIED EXTRAGRADIENT-TYPE METHODS FOR SOLVING VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS

In this paper, we propose two new modified extragradient-type methods for finding a common element of fixed points set of a nonexpansive mapping and the solutions set of a variational inequality problem in Hilbert space. In our methods, on every iteration, we use only two projections onto some simple closed convex set C. Under the assumptions that the mapping in variational inequality problem is continuous(not necessary Lipschitz continuous) and monotone, we prove strong convergence theorems of the proposed algorithms. Preliminary computational experience is also reported.