ON THE BOUNDED SLOPE CONDITION

λ. Hence, if dΩ e C1'1 is uniformly convex, then φ(x)y xedΩ, satisfies a bounded slope condition if and only if φ(x)eC1>ι. The proofs use generalized convex functions of Beckenbach and, if n > 2, the equivalence of the bounded slope condition and an "(n + l)-point condition".