When Is the Product of Two Concave Functions Concave ?
نویسندگان
چکیده
In this paper we prove the following results concerning the product f1f2 of two concave functions f1and f2 defined in a non empty, compact, convex set K of R. The first result states that necessary and sufficient condition for the product f1f2 of two linear affine functions to be concave is that they are Gonzi. Finally the main result says that a necessary and sufficient condition for the product of two positive functions f1 and f2 to be concave is that same associated linear function be Gonzi. As an application we prove that the minimax theorem for product of bilinear functions.
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