Abstract
Many theorems in convex analysis and quasi-variational inequalities can be derived by using a class of weaker convexity (concavity) conditions which require a functional φ( x, y) to be quasi-convex or convex for diagonal entries of certain type. In this paper, we discuss such conditions and use them to generalize several important theorems such as Ky Fan's inequality and saddle point theorem and some recent results in quasi-variational inequalities.
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