The author introduces a new class of non-convex functions: The function is said to be -convex, if there exists a function such that
where is a -convex set. It is proved that the minimum of differentiable -convex functions can be characterized by a class of variational inequalities, which is called the general variational inequality. Using the projection technique, the equivalence between the general variational inequalities and the fixed-point problems as well as with the Wiener-Hopf equations is established. This equivalence is used to suggest and analyze some iterative algorithms for solving the general variational inequalities.