CONVEXITY PRESERVING SCALE TRANSFORMATIONS,

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)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1969
Accession Number
AD0701156

Entities

People

  • Albert W. Marshall
  • Frank Proschan

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Contract Administration
  • Contracts
  • Functions (Mathematics)
  • Intervals

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.