On a generalization of Mulholland's inequality
The author offers as main result the following. Let \(g\) be a convex homeomorphism of the nonnegative reals, such that also \(\log\circ g\circ\exp\) be convex. Then for all nonnegative \(x_ k\), \(y_ k\) and for all \(a_ k\) not smaller than 1 \((k=1,\dots,n)\), \[ g^{- 1}\left(\sum^ n_{k=1} a_ k g(x_ h+ y_ k)\right)\leq g^{- 1}\left(\sum^ n_{k=1} a_ k g(x_ k)\right)+ g^{-1}\left(\sum^ n_{k=1} a_ k g(y_ k)\right). \] As a consequence, in a result of the author in Proc. Am. Math. Soc. 190, No. 3, 663-675 (1990; Zbl 0704.46020) the following requirement cannot be dropped: there exists a set of measure strictly between 0 and 1 in the measure space there defined.
scientific article; zbMATH DE number 492586