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Let K be a nonempty closed convex subset of a real Hilbert space H . Approximationsolvability of a class of relaxed γ r -cocoercive nonlinear variational inequality (NVI) problems, based on the convergence of projectionmethods, is discussed as follows: find an elements x∗ ∈ K such that 〈 T(x∗), x − x∗〉 0 ∀x ∈ K where T : K → H ia a nonlinear mapping on K . Mathematics subject classification (2000): 49J40, 65B05, 47H17.

A class of relaxed γ-r-cocoercive nonlinear variational inequalities and convergence of projection methods