Affine and convex functions with respect to the logarithmic mean

Volume 95 / 2003

Janusz Matkowski Colloquium Mathematicum 95 (2003), 217-230 MSC: Primary 26E60, 26B25; Secondary 39B62. DOI: 10.4064/cm95-2-6

Abstract

The class of all functions $f:(0,\infty )\rightarrow (0,\infty )$ which are continuous at least at one point and affine with respect to the logarithmic mean is determined. Some related results concerning the functions convex with respect to the logarithmic mean are presented.

Authors

  • Janusz MatkowskiInstitute of Mathematics
    University of Zielona Góra
    Podgórna 50
    65-246 Zielona Góra, Poland
    e-mail

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