
Accession Number : AD0701156
Title : CONVEXITY PRESERVING SCALE TRANSFORMATIONS,
Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
Personal Author(s) : Marshall,Albert W. ; Proschan,Frank
Report Date : DEC 1969
Pagination or Media Count : 18
Abstract : Let C be the class of increasing convex functions on the interval from zero to (but less than) infinity with f(0) = 0. Then f epsilon C implies that the composition (psi)f(psi superscript1) epsilon C if and only if psi(x) = c(x to the power p), c > 0, p = or > 1. Functions psi for which (psi)f(psi superscript1) epsilon C whenever f epsilon C are characterized for various other classes C, e.g., the concave, starshaped or superadditive increasing functions f on the interval from zero to (but less than) infinity with f(0) = 0. In addition, classes of functions on other domains, and logarithmically convex or concave functions are also considered. (Author)
Descriptors : (*FUNCTIONS(MATHEMATICS), *TRANSFORMATIONS(MATHEMATICS)), RELIABILITY, SET THEORY, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE