Let C be a nonempty, closed and convex subset of a 2-uniformly convex and uniformly smooth real Banach space E. Let T: C→ C be relatively nonexpansive mapping and let Ai: C→ E* be Li-Lipschitz monotone mappings, for i = 1,2. In this paper, we introduce and study an iterative process for finding a common point of the fixed point set of a relatively nonexpansive mapping and the solution set of variational inequality problems for A1 and A2. Under some mild assumptions, we show that the proposed algorithm converges strongly to a point in F(T) ∩ VI(C, A1) ∩ VI(C, A2). Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
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