Vol. 22, No. 2, 1967

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An inequality for generalized means

Harry Wright McLaughlin and Frederic Thomas Metcalf

Vol. 22 (1967), No. 2, 303–311

This paper is concerned with the behavior of certain combinations of generalized means of positive real numbers, considered as functions of the index set. It is shown that these combinations are actually superadditive functions (over set unions) of the index set. Several previously established inequalities of this nature are obtained as corollaries of the main theorem, namely, certain results of R. Rado, W. N. Everitt, D. S. Mitrinovič and P. M. Vasič, and H. Kestleman.

Mathematical Subject Classification
Primary: 26.70
Received: 10 February 1967
Published: 1 August 1967
Harry Wright McLaughlin
Frederic Thomas Metcalf