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Numerous strong and weak convergence results on variational inequality problems are known in the literature. We here study a variational inequality problem by using the viscosity approximation method in the nonlinear CAT(0) space, where some novel theorems are established for strong and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-convergent sequences.