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 superscript-1) 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 superscript-1) 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