The question of whether cone metric spaces are real generalizations of metric spaces is proved, in the sense of Best Approximation, not to be affirmative.
In this paper we prove that if ? is a modulus function and if X = [0,1] is given the Lebesgue measure, then M(L?) = L?, if and only if lim x – 0 ?(x2)/ ?(x) < ?; L? being the Orlicz space L? (X); and M(L?) its multiplier algebra.