Parallel hybrid iterative methods for variational inequalities, equilibrium problems and common fixed point problems

Abstract: 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 $\phi$-asymptotically nonexpansive mappings ${F(S_j)}{j=1}^N$, the set of solutions of variational inequalities ${VI(A_i,C)}{i=1}^M$ and the set of solutions of equilibrium problems ${EP(f_k)}_{k=1}^K$ in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify the efficiency of the proposed parallel algorithms.