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We propose a new approach to study variational relation problems. Namely, we apply Mizoguchi and Takahashi’s fixed point theorem of contraction mappings and an error bound of a system of linear inequalities to establish existence conditions for a variational relation problem in which the variational relation linearly depends on the decision variable. Then we develop an algorithm to compute a solution of a linear variational relation problem.

Variational relation problems: existence of solutions and fixed points of contraction mappings