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In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of nonexpansive mappings and the set of solutions of generalized variational inequalities for a k-strict pseudo-contraction by relaxed extra-gradient methods. Strong convergence theorems are established in q-uniformly smooth Banach spaces.

STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS IN q-UNIFORMLY SMOOTH BANACH SPACES