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A computational role of a class of partially relaxed monotone mappings in the approximation-solvability of a class of nonlinear variational inequalities based on a variational inequality type algorithm is presented. We consider a class of nonlinear variational inequality (abbreviated as NVI) problems: find an element x∗ ∈ K such that 〈 T(x∗), x − x∗〉 0 for all x ∈ K, where T : K → H is a γ -r-partially relaxed monotone mapping and K a closed convex subset of a real Hilbert space H . Mathematics subject classification (2000): 49J17, 65B05.

A computational role of partially relaxed monotone mappings in approximation solvability of nonlinear variational inequalities