Abstract:  In this paper,applying the concept of generalized KKM map,we study problems ofvariational inequalities.We weaken convexity(concavity)conditions for a functional of two variables■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree method of acute angle principle about monotone operator as an application of these results.

Key words:  , generalized ,  , KKM , map, upper ,  , (lower)-semi-continouous, T-diagonally ,  , quasi- wnvex(concave)monotone operator