MathDB

For each

t \geq 0

let

S_t

be the set of all nonnegative, increasing, convex, continuous, real-valued functions

f(x)

defined on the closed interval

[0,1]

for which f(1) -2 f(2 \slash 3) +f (1 \slash 3) \geq t( f( 2 \slash 3) -2 f(1 \slash 3) +f(0)). Define necessary and sufficient conditions on

t

for

S_t

to be closed under multiplication.

B5