In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and Lipschitz continuous operators. Based on differently constructed half-spaces, the proposed methods reduce the number of projections onto feasible sets as well as the number of values of operators needed to be computed. Strong convergence theorems are established under standard assumptions imposed on the operators. An extension of the proposed algorithm to a system of generalized equilibrium problems is considered and numerical experiments are also presented.

In this paper we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of quasi φ-asymptotically nonexpansive mappings {F (S j )} N j=1 , the set of solutions of variational inequalities {V I(A i , C)} M i=1 and the set of solutions of equilibrium problems {EP (f k )} K k=1 in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify the efficiency of the proposed parallel algorithms.

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In this paper we study some novel parallel and sequential hybrid methods for finding a common fixed point of a finite family of asymptotically quasi φnonexpansive mappings. The results presented here modify and extend some previous results obtained by several authors.