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Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities. (English) Zbl 0649.49008

The authors generalize several theorems in convex analysis (Ky Fan’s inequality, saddle point theorem) and quasi-variational inequalities by using weaker convexity (concavity) conditions. These conditions require a functional \(\Phi(x,y)\) to be (quasi-) convex for diagonal entries of certain type.
Reviewer: P.Quittner

MSC:

49J35 Existence of solutions for minimax problems
49J40 Variational inequalities
49J27 Existence theories for problems in abstract spaces
90C25 Convex programming
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