> 0. Condition (ii) implies that h is convex,

Ifwetake y = 0, ~ = 1/o. > 0 and h(z) = e..tz, with 1 < lA. I$ rt/2, then P(z) = e..tz/o. satisfies (i) and (iii). The domain P(U) is lima-bean shaped and is clearly not convex. Thus condition (ii) is not satisfied in this case, but

we still have

If we let <jl[w] = ~w + y and <jl[w] = (~w + y)-2 in Theorem 3.4a we obtain the following two corollaries.